POLYGONS and AREA
Classifying Polygons
Angles in Polygons
Area of Squares and Rectangles
Area of Triangles
Area of Parallelograms
Area of Trapezoids
Circumference and Area of Circles
OPENERS
Assignments
Reviews
POLYGONS and AREAClassifying Polygons
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POLYGON BASICS
When people use the word “SHAPE” they are usually referring to a POLYGON.
So, what is a POLYGON?
Basically, it is a CLOSED shape with “straight” sides
POLYGONS and AREAClassifying Polygons
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CLOSED means the shape is complete
closed
NOT closed
POLYGONS and AREAClassifying Polygons
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Straight Sides No curves
“Straight”
Curved
POLYGONS and AREAClassifying Polygons
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What do all these shapes
have in common?
They are all simple
polygons.To be a polygon you need 2 things:
CLOSED STRAIGHT
POLYGONS and AREAClassifying Polygons
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Why do we need to know about polygons?
Polygons show up all over in nature, science, engineering…
POLYGONS and AREAClassifying Polygons
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If you play video games…
You may have seen the word POLYGONS, and know it has something to do with graphics.
This is because C.A.D. programs use polygons to render objects C. computer
A. aidedD. drafting
Make a 3-D model
POLYGONS and AREAClassifying Polygons
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POLYGONS and AREAClassifying Polygons
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POLYGONS are the basis of most computer imaging.
The more POLYGONS and image has, the higher the quality
POLYGONS and AREAClassifying Polygons
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Before we do anything with polygons, you must understand the difference between CONVEX and CONCAVE.
Convex Concave
POLYGONS and AREAClassifying Polygons
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It is easier to explain CONCAVE than it is to explain CONVEX
A polygon is CONCAVE if:
There are 2 points somewhere inside the shape
So that if you connect those 2 points with a line
The line goes outside the shape.
POLYGONS and AREAClassifying Polygons
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These are all CONCAVE
It may help to think of CONCAVE as having a “cave”or indentation
POLYGONS and AREAClassifying Polygons
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If you cannot find 2 points that make a line that goes outside . . .
Then the shape is CONVEX
POLYGONS and AREAClassifying Polygons
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And if any of the lines go back into the shape, then it is CONCAVE
Another way to determine if a polygon is CONVEX or CONCAVE is to extend all the sides…
POLYGONS and AREAClassifying Polygons
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CONCAVECONCAVE CONCAVE
CONVEX CONVEX CONCAVE
CONVEX CONVEX CONCAVE
POLYGONS and AREAClassifying Polygons
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CONVEX or CONCAVE?
These two aren’t even POLYGONS, why?
They have curves.
POLYGONS and AREAClassifying Polygons
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In regular geometry, CONCAVE shapes are like your strange cousin.
We just don’t talk about them.
We will spend almost all of our time on CONVEX shapes
CONCAVE IS BAD!!
POLYGONS and AREAClassifying Polygons
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What do we call a polygon with three sides?
A triangle
POLYGONS and AREAClassifying Polygons
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What do we call a shape with four sides?A quadrilateral
POLYGONS and AREAClassifying Polygons
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What do we call a shape with five sides?A pentagon
POLYGONS and AREAClassifying Polygons
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What do we call a shape with six sides?A hexagon
POLYGONS and AREAClassifying Polygons
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What do we call a shape with seven sides?A heptagon (sometimes also called a septagon)
POLYGONS and AREAClassifying Polygons
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What do we call a shape with eight sides?
An octagon
POLYGONS and AREAClassifying Polygons
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A nine sided figure is called …
A nonagon
A ten sided figure is called …
A decagon
POLYGONS and AREAClassifying Polygons
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While the shapes with more than 10 sides have names, it is acceptable to call them “n-gons”
What does THAT mean?
It means you can call an eleven sided shape an “11-gon”
and a twenty-three sided polygon a “23-gon”
POLYGONS and AREAClassifying Polygons
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In a REGULAR polygon…
All the sides are congruent,
All the angles are congruent3
3
3
3
3
1080
1080 1080
1080
1080
EQUILATERAL
EQUIANGULAR
POLYGONS and AREAClassifying Polygons
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No matter how many sides the polygon has, they all have the same parts.
SIDEVERTEX
(vertices)
POLYGONS and AREAClassifying Polygons
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Naming any polygon has 1 simple rule:Pick any 1 vertex to start,
BC
D
EF
G
A
Then go around the shape, clockwise OR counterclockwise
heptagon BCDEFGAheptagon FEDCBAGTo keep it simple we will try to go as close to alphabetical as we can
heptagon ABCDEFG
POLYGONS and AREAClassifying Polygons
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POLYGONS and AREAClassifying Polygons
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PERIMETER is the distance around the outside of a 2-D object
In other words:If you walked around a polygon, how far would you walk?
POLYGONS and AREAClassifying Polygons
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What is the perimeter of this rectangle?
4
12
12
4
Perimeter: 12 + 4 + 12 + 4OR 2(12 + 4)
= 32
POLYGONS and AREAClassifying Polygons
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Find the perimeter for each of the following polygons:
4
7
4
7
3
2
3 44 4
44
444
44
31
3 3
3
1
111
1
11
75
2
2
4
2
11
11
11
11
11
228 40
20
22
55
1.
2.
3.
4.
5.
6.
POLYGONS and AREAClassifying Polygons
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Find the perimeter for the following REGULAR polygons:
2
20
40 24
60
7.
8.
9.
8
12-gon
POLYGONS and AREAClassifying Polygons
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10. Find the perimeter of a regular nonagon with side lengths of 13?
11. Find the perimeter of a regular 27-gon with side lengths of 6?
117
162
POLYGONS and AREAAngles in Polygons
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Interior and
Exterior angles in
Polygons
POLYGONS and AREAAngles in Polygons
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The INTERIOR ANGLES of a polygon are the angles inside the figure
POLYGON ANGLES
We know the angles of a triangle add to 180.
In the other shapes, we draw in triangles to find the angle sum.
180
180
180 =360 18
018
0
180
=540
180 18
0
180
180
=720
180
180
180
180
180
180
=1080
POLYGONS and AREAAngles in Polygons
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INTERIOR ANGLESTHEOREM: The Sum of the INTERIOR
angles of a convex polygon is (n-2) x 180.(n is the number of sides)
So in a pentagon (5 sides), n=5
The sum of the interior angles:(5-2) x 180
3 x 180
540
POLYGONS and AREAAngles in Polygons
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INTERIOR ANGLE
PROBLEMS
POLYGONS and AREAAngles in Polygons
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1. In a quadrilateral, what is the sum of the interior angles?
2. In a hexagon, what is the sum of the interior angles?
3. In a decagon, what is the sum of the interior angles?
180)24( 360
180)26( 720
180)210( 440,1
POLYGONS and AREAAngles in Polygons
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4.70
90150
x
)1509070(360
50
5.
100
z
110
120105
)100105120110(540 105
POLYGONS and AREAAngles in Polygons
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6.
7.
All the angles in the given shape are equal. Find X & Y
All the angles in the given shape are equal. Find X & Y
180180)23(
603180
12060180
Sum of the interior angles
Each of the interior angles
Each exterior angle60120
1080180)28(
13581080
45135180
Sum of the interior angles
Each of the interior angles
Each exterior angle13545
POLYGONS and AREAAngles in Polygons
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8. In a regular, convex 12-gon, what is the measure of each interior angle?
9. In a regular, convex 12-gon, what is the measure of each exterior angle?
(12 2) 180 1800 1800
15012
Each interior angle is 150…
So each exterior angle is 30.
What is an EXTERIOR angle?
EXTERIOR ANGLESTHEOREM: The Sum of the EXTERIOR
angles of a convex polygon is 3600
That’s what you get when you extend all the sides in the same direction.
POLYGONS and AREAAngles in Polygons
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What is the sum of the exterior angles of an octagon? 360What is the sum of the exterior angles of a pentagon? 360What is the sum of the exterior angles of a decagon? 360
EXTERIOR ANGLESTHEOREM: The Sum of the EXTERIOR
angles of a convex polygon is 3600
POLYGONS and AREAAngles in Polygons
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POLYGONS and AREAAngles in Polygons
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90
68
80
X
63
110
117
X
90 + 68 + 80 + X + 63 = 360 127 + 119 + X = 360
301 + X = 360
X = 59
246 + X = 360
X = 133
13. 14.
POLYGONS and AREAAngles in Polygons
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15. What is the measure of an exterior angle of a REGULAR octogon?
16. What is the measure of an exterior angle of a REGULAR decagon?
17. What is the measure of an exterior angle of a REGULAR 36-gon?
18. What is the measure of an exterior angle of a REGULAR 100-gon?
03608
045
036010
036
036036
010
0360100
03.6
POLYGONS and AREAAngles in Polygons
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2x
2x+5
x+152x+10
3x-10
3x-10+2x+2x+5+x+15+2x+10 = 360
10x+20 = 360
10x = 340
x = 34
19. FIND X:
POLYGONS and AREAAngles in Polygons
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X
20. The picture shows a REGULAR HEXAGON. Find X: 0360
6060
POLYGONS and AREAAngles in Polygons
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21. A regular polygon with an unknown number of sides has exterior angles measuring 200. How many sides does it have?
36020
XX X
360 20x20 20
18 x
POLYGONS and AREAArea of Squares and Rectangles
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AREA of
RECTANGLES
POLYGONS and AREAArea of Squares and Rectangles
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Area is a measure of “flat space”.
If you wanted to cover a floor with 1ft by 1ft tiles, the area of the floor is the number of tiles it takes to cover the floor.
POLYGONS and AREAArea of Squares and Rectangles
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It is 10 feet long
Here is a small room:
and 6 feet wide
10
6
To cover the room with 1x1 tiles . . .
10 acrossby 6 deep
1
1
POLYGONS and AREAArea of Squares and Rectangles
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10
6
You need 10 of them across
And 6 deep
POLYGONS and AREAArea of Squares and Rectangles
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For each of the 10 across, there are 6 deep
10
6
How many total tiles?6 x 10 = 60
This is where base x height comes from
ft
ft
POLYGONS and AREAArea of Squares and Rectangles
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10
6
Because area is measured by how many “squares” fit in a polygon…
We call the units in area “SQUARE UNITS”
Area is “60 square feet”.
260Area f t
POLYGONS and AREAArea of Squares and Rectangles
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Formula for the area of a rectangle:
B
HArea Base Height
*Base and height always make a right angle.
POLYGONS and AREAArea of Squares and Rectangles
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Find the AREA and PERIMETER of each of the following:
1. 2.
70in
35in
14m
70 35Area 22,450in
70 35 70 35Perimeter 210in
14 14Area 2196m
14 14 14 14Perimeter 56m
POLYGONS and AREAArea of Squares and Rectangles
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3. Find the area of the shape shown.
12
9
3
3
To do this, find the area of the big blue piece (pretend it doesn’t have a hole in it)
Then find the area of the “cutout”
Finally, subtract them.
9 12A 108 2u
3 3A 9 2u
108 9 299u
POLYGONS and AREAArea of Squares and Rectangles
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4. Find the AREA and PERIMETER of the shape shown.
6cm
2cm1cm
2cm
1cm
12cm
6cm
Perimeter is easy, just add up the sides.
The only trick is that you have to make sure you have all the sides.
6 2 1 2 6 8 1 12P
8cm 38cm
POLYGONS and AREAArea of Squares and Rectangles
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4. Find the AREA and PERIMETER of the shape shown.
6cm
2cm1cm
2cm
1cm
12cm
6cm
8cm
To find the area, cut the shape into parts you can work with
22cm
224cm
28cm
2 24 8A 234cm
POLYGONS and AREAArea of Squares and Rectangles
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4. Find the AREA and PERIMETER of the shape shown.
6cm
2cm1cm
2cm
1cm
12cm
6cm
8cm
To find the area, cut the shape into parts you can work with
210cm
212cm
212cm
12 12 10A 234cm
POLYGONS and AREAArea of Triangles
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AREA of TRIANGLES
POLYGONS and AREAArea of Triangles
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Find the area of the rectangle shown:
4m
10
m
4m
10
m
Area = BxH
=4x10
=40m2
4m
10
m
4m
10
m
Each of these triangles is HALF the area of the original rectangle.
20m2
20m2
POLYGONS and AREAArea of Triangles
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What if it is not a right triangle?
POLYGONS and AREAArea of Triangles
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No matter the type of triangle… …It is still HALF of a RECTANGLE.
b
h
POLYGONS and AREAArea of Triangles
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Formula for finding the area of a triangle:
12
A b h
*Base and height always make a right angle.
b
h
b b
hh
POLYGONS and AREAArea of Triangles
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Find the AREA and PERIMETER for each of the following triangles:
5m3m
4m
EXAMPLE #1
To find the area, we need base and height
hbArea 2
1
Remember the base and height make a right angle with each other.
342
1Area 26m
For perimeter, just add all the sides:
543 Perimeterm12
POLYGONS and AREAArea of Triangles
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Find the AREA and PERIMETER for each of the following triangles:
15ft
8ft17ft
EXAMPLE #2
hbArea 2
1
8152
1Area 260 ft
For perimeter, we need to know that 3rd side.
We can find it using the PYTHAGOREAN THEOREM
2 2 28 15 c 17 c
8 15 17Perimeter ft40
POLYGONS and AREAArea of Triangles
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Find the AREA and PERIMETER for each of the following triangles:
10 10
12
8EXAMPLE #3
hbArea 2
1
1282
1Area 248u 101012 Perimeter
u32
POLYGONS and AREAArea of Triangles
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STUDENT PROBLEMS
1#
Find the AREA and PERIMETER for each of the following triangles 2#
12m
16m20m
24ft
10ft
161221: A
296m
201612: Pm48
26
102421: A
2120 ft
262410: P60f t
POLYGONS and AREAArea of Triangles
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Find the AREA for this triangle
5
8
712
EXAMPLE #4This is an easy one…
…Sometimes the height is outside the triangle…
…but that doesn’t change anything.
hbArea 2
1
582
1Area 220u
12 8 7Perimeter 27u
POLYGONS and AREAArea of Triangles
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Find the AREA for this triangle
26 26
48
EXAMPLE #5
This triangle is isosceles.
That means the height to the base bisects the base.
24 24
We need to find the height.
h
We will have to use the PYTHAGOREAN THEOREM to find the height. 222 2624 h
10h
10
hbArea 2
1
10482
1Area 2240u
POLYGONS and AREAArea of Triangles
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STUDENT PROBLEMS
Find the AREA and PERIMETER for each of the following triangles3#
16in
17in17in
151621: A
2120in
171716: Pin50
15
8
4#
6
594
3
6421: A
212u
965: Pu20
POLYGONS and AREAArea of Triangles
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Find the area of this shape:
12in
9in 14in
12in
13in5in
30in2
108in2
138in2
EXAMPLE #6
POLYGONS and AREAArea of Triangles
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STUDENT PROBLEMS
Find the AREA of the following shape.5#
17in
15in
9in
17in 15
8
135
60
2135 60 195in
POLYGONS and AREAArea of Triangles
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These 2 triangles are similar, with a scale factor of
If the area of the big one is 50cm2 then what is the area of the small one?
35
20cm
5cm
12cm
3cm
13 12
2A
18
EX
AM
PLE
#7
POLYGONS and AREAArea of Triangles
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These 2 triangles are similar, with a scale factor of
If the area of the big one is 100cm2 then what is the area of the small one?
35
X
Y
X5
3
Y5
3
XYArea2
1100 Area
5
3 YX
5
3
2
1
EX
AM
PLE
#7
POLYGONS and AREAArea of Triangles
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These 2 triangles are similar, with a scale factor of
If the area of the big one is 100cm2 then what is the area of the small one?
35
X
Y
X5
3
Y5
3
XYArea2
1100 Area
5
3 YX
5
3
2
1Area
5
3 YX
5
3
2
1
2100sArea
3 3100
5 5Area
36Area
POLYGONS and AREAArea of Triangles
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Finding the AREA of SIMILAR POLYGONS
If 2 polygons are similar, the ratio of their areas is the square of the scale factor
Area = 36m2
These 2 polygons are similar.The scale factor is
3
2
If the area of the big one is 36, find the area of the other.
3
2
3
236 Area
216m
POLYGONS and AREAArea of Triangles
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STUDENT PROBLEMS
ABCDEofareathefindUWXYZABCDE ,~
E
A
B
CD
Z
U
W
XY
A: 54m2
68
First, find the scale factor4
3
8
6
Multiply the area by the scale factor twice 3
4
3
454 296m
6#
POLYGONS and AREAArea of Triangles
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Find the area of this regular pentagon
8
12
10
6
24
EXAMPLE #8
POLYGONS and AREAArea of Triangles
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Find the area of this regular pentagon
8
12
10
6
242424
24
24
24
24 24
24
24
24
Area = 24x10
=240u2
EXAMPLE #8
POLYGONS and AREAArea of Triangles
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STUDENT PROBLEMS
Find the AREA of this regular octogon:
10m
12m
5
Area of 1 triangle:
# of triangles:
30
16
Area: 30x16=480m2
7#
POLYGONS and AREAArea of Parallelograms
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Area of PARALLELOGRAMS
POLYGONS and AREAArea of Parallelograms
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To calculate the area of a parallelogram…
Just Multiply base and height
B
H
Area of a Parallelogram
hbArea h
b*Base and height make a right angle.
POLYGONS and AREAArea of Parallelograms
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Area of a
RHOMBUS
POLYGONS and AREAArea of Parallelograms
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d1
d2
Calculating the area of a rhombus can be done the same as a parallelogram…OR you can use the
diagonals
POLYGONS and AREAArea of Parallelograms
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d1
d2
Calculating the area of a rhombus can be done the same as a parallelogram…OR you can use the
diagonals
This rectangle has an area of
A = d1 x d2
So each Rhombus is half that.
POLYGONS and AREAArea of Parallelograms
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•It does NOT matter which diagonal is which.
•Remember the diagonal goes all the way across the shape.
•You will frequently be given only half of a diagonal.
Area of a Rhombus
212
1ddArea
*the diagonals always make a right angle.
d1
d 2
POLYGONS and AREAArea of Parallelograms
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Find the area of each Parallelogram
#1 #2
10ft
20ft
8ft
16cm
7cm
22cm
hbA 208 2160 ft
hbA 167 2112cm
POLYGONS and AREAArea of Parallelograms
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Find the area of each Rhombus
#3 #4 #5
3m4m
127
10ft
20ft 12
7
212
1ddA
862
1A
224mA
20102
1A
2100 ftA
14242
1A
2168A u
POLYGONS and AREAArea of Trapezoids
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Area of a
Trapezoid
POLYGONS and AREAArea of Trapezoids
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This is a trapezoid: It has 1 set of parallel sides.
The MIDSEGMENT …
Joins the midpoints of the legs
Base1
Base2Le
g Leg
Has a length that is the average of the bases
211 bb
midsegment
POLYGONS and AREAArea of Trapezoids
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Like most shapes, the area of a trapezoid is based on a rectangle
midsegment:
heig
ht:
Base1
Base2
POLYGONS and AREAArea of Trapezoids
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Area of a Trapezoid
heightmidsegmentArea
hbb
2
21
1b
2b
h
POLYGONS and AREAArea of Trapezoids
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Find the area of each of the following trapezoids:
#1 #2 #3
8m
6m
7m 12mi
11mi
6mi
13mi
9
15
8
10
72
68
A
249m
122
611
A
2102mi
82
159
A
296u
POLYGONS and AREAArea of Trapezoids
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Find the area of this shape:
22
10
11
2022
9
242
144144 + 242 =
386u2
POLYGONS and AREAArea of Trapezoids
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Find the area:
POLYGONS and AREAArea of Trapezoids
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Find the area:
POLYGONS and AREAArea of Trapezoids
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Find the area:
POLYGONS and AREAArea of Trapezoids
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Find the area:
POLYGONS and AREAArea of Trapezoids
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Find the area:
POLYGONS and AREAArea of Trapezoids
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Find the area:
POLYGONS and AREAArea of Trapezoids
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Find X:
POLYGONS and AREAArea of Trapezoids
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Find X:
POLYGONS and AREAArea of Trapezoids
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Find X:
POLYGONS and AREAArea of Trapezoids
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Find X:
POLYGONS and AREAArea of Trapezoids
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Find X:
POLYGONS and AREAArea of Trapezoids
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Find X:
POLYGONS and AREAArea of Trapezoids
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Find X:
POLYGONS and AREAArea of Trapezoids
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Find X:
POLYGONS and AREAArea of Trapezoids
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Find X:
POLYGONS and AREACircumference and Area of Circles
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RadiusDiameterChordSecantTangentPoint of Tangency
Distance from center to edge of a circleDistance from edge to edge of a circle through the
centerAny line segment that goes from edge to edge in a
circleAny line that passes through a circle
A line that touches the circle at exactly 1 point
The point where a circle an tangent touch
POLYGONS and AREACircumference and Area of Circles
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RadiusDiameterChordSecantTangentPoint of Tangency
C
A
BD
E
F
G
H
J
POLYGONS and AREACircumference and Area of Circles
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RadiusDiameterChordSecantTangentPoint of Tangency
C
A
BD
E
F
G
H
AC
J
POLYGONS and AREACircumference and Area of Circles
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RadiusDiameterChordSecantTangentPoint of Tangency
C
A
BD
E
F
G
H
BD
J
POLYGONS and AREACircumference and Area of Circles
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RadiusDiameterChordSecantTangentPoint of Tangency
C
A
BD
E
F
G
H
ED
J
POLYGONS and AREACircumference and Area of Circles
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RadiusDiameterChordSecantTangentPoint of Tangency
C
A
BD
E
F
G
H
GH
J
POLYGONS and AREACircumference and Area of Circles
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RadiusDiameterChordSecantTangentPoint of Tangency
C
A
BD
E
F
G
H
JF
J
POLYGONS and AREACircumference and Area of Circles
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RadiusDiameterChordSecantTangentPoint of Tangency
C
A
BD
E
F
G
H
F
J
POLYGONS and AREACircumference and Area of Circles
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For a circle, the formulas for area and perimeter are different, because there are no sides and there is no base or height.
POLYGONS and AREACircumference and Area of Circles
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5
Radius:
Diameter:
Circumference:
The distance from the center of a circle to the edge
The distance from edge to edge of a circle, passing through the center
10
The distance around the outside of a circle
POLYGONS and AREACircumference and Area of Circles
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10
What is pi Pi is what you get if you divide the distance around the outside of any circle by that circles diameter
POLYGONS and AREACircumference and Area of Circles
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Area of a circle:
Circumference of a circle:
2rA
rC 2
5
25A
25
52C10
POLYGONS and AREACircumference and Area of Circles
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8
Find the area and circumference:
AREA CIRCUMFERENCE2rA 28A
64A
rC 2
82C
16C
POLYGONS and AREACircumference and Area of Circles
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12
Find the area and circumference:
AREA CIRCUMFERENCE2rA 26A
36A
rC 2
62C
12C
6
Notice that this is just the diameter times pi.
DrC 2
POLYGONS and AREACircumference and Area of Circles
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FINDING ARCLENGTH
Here is a slice of pizza.
60
6It has a 6 inch radius,And we cut a 60 degreeSlice out of it.
How much crust do you have ?
The crust of the whole pizza:(circumference)
rC 2 62 12
68.37
But you don’t have the wholePizza, you just have 60 degrees
360
6068.37 inches28.6
POLYGONS and AREACircumference and Area of Circles
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To find ARCLENGTH
360
2angle
rarclength120
8
360120
82
7.16
POLYGONS and AREACircumference and Area of Circles
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Find the arclength.
70
5
360
2angle
rarclength
360
7052
1.6
POLYGONS and AREACircumference and Area of Circles
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Find the area of the SECTOR
POLYGONS and AREACircumference and Area of Circles
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2rArea of the whole circle:
Area of a sector or “slice”:
2
360
angler 2
360r
2 606
360 218.84in
Find the area of the SECTOR
POLYGONS and AREACircumference and Area of Circles
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2
360r
2 9010
360
278.5f t
POLYGONS and AREAOPENERS
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ABCDEFGHIJKLMNOPQRS
TUVWXYZ
POLYGONS and AREAOPENERS A
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POLYGONS and AREAOPENERS B
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POLYGONS and AREAOPENERS C
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POLYGONS and AREAOPENERS D
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POLYGONS and AREAOPENERS E
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POLYGONS and AREAOPENERS F
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POLYGONS and AREAOPENERS G
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Can you do this WITHOUT
a CALCULATOR?
POLYGONS and AREAOPENERS H
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In your job as a cashier, a customer gives you a $20 bill to pay for a can of coffee that costs $3.84. How much change should you give back?
a) $15.26 b) $16.16 c) $16.26 d) $16.84 e) $17.16
POLYGONS and AREAOPENERS I
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How much time is there between 7:35 a.m. and 5:25 p.m.?
a) 8 hours and 50 minutesb) 9 hours and 10 minutesc) 9 hours and 50 minutesd) 10 hourse) 10 hours and 50 minutes
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POLYGONS and AREAOPENERS K
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POLYGONS and AREAOPENERS L
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POLYGONS and AREAReviews
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Find the Area (assorted)Compound Polygon (5-Questions)Jeopardy ReviewReview for Quiz 8.1-8.2Review for Quiz 8.3-8.5Review Harder Problems
Geoemtry NAME ______________________ Find the area of each composite shape shown. All angles are right. 1. 2. 3. 4.
5.
Geoemtry NAME ______________________ Find the area of each composite shape shown. All angles are right. 1. 2. 3. 4.
5.
POLYGONS and AREAReviews
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Find the area of each shape:1 2 3 4
5 6 7 8
9 10 11
24 6 12154
69 28 31 126
12
29 52
3
answers
500500500500500
400 400400400400400
500
300300300300300300
200200200200200200
100100100100100100
Column 6Column 5Column 4Column 3Column 2Column 1
POLYGONS and AREAReviews
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Geoemtry NAME ______________________ Find the area of each composite shape shown. All angles are right. 1. 2. 3. 4.
5.
POLYGONS and AREAReviews
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Geoemtry NAME ______________________ Find the area of each composite shape shown. All angles are right. 1. 2. 3. 4.
5.
POLYGONS and AREAReviews
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POLYGONS and AREAReviews
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Review for quiz 8.1-8.2
VOCABULARY: Equilateral, Equiangular, Regular, Triangle, Quadrilateral, Pentagon, Hexagon, Heptagon, Octagon, Nonagon, Decagon, Convex, Concave, Interior, Exterior
POLYGONS and AREAClassifying Polygons
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Identify as CONVEX or CONCAVE
POLYGONS and AREAClassifying Polygons
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What is the sum of the interior angles of a decagon?
What is the sum of the exterior angles of a pentagon?
x4
POLYGONS and AREAClassifying Polygons
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Find X
x4
90
68
80
X
63
90 + 68 + 80 + X + 63 = 360
301 + X = 360
X = 59
130
110 112
138
X113
X+113+130+110+112+138=720
X=117
POLYGONS and AREAClassifying Polygons
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What is the measure of each interior angle of a regular 30-gon?
What is the measure of each exterior angle of a regular hexagon?
x4
A regular polygon has exterior angles measuring 150. How many sides does it have?
POLYGONS and AREAReview 8.3-8.5
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POLYGONS and AREAReview 8.3-8.5
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POLYGONS and AREAReview 8.3-8.5
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POLYGONS and AREAReview 8.3-8.5
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POLYGONS and AREAReview HARDER PROBLEMS
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#1 Find the area of the RED region
POLYGONS and AREAReview HARDER PROBLEMS
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#2 Find the measure of X.
POLYGONS and AREAReview HARDER PROBLEMS
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#3 Find the area:
POLYGONS and AREAReview HARDER PROBLEMS
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#4
POLYGONS and AREAReview HARDER PROBLEMS
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#5 Find the measure of the area of the sector.
POLYGONS and AREAReview HARDER PROBLEMS
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#6 The area of the square shown is 144 in2. Find the length of the sides.
POLYGONS and AREAReview HARDER PROBLEMS
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#7 Find X if the area of the trapezoid is 48in2:
X
4in
12in
POLYGONS and AREAReview HARDER PROBLEMS
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#8 Find the area of the RED region: