copyright©amberpasillas2010. perimeter – (p) (p) the distance around a figure. 10 ft. 6 ft. 10 6...
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copyright©amberpasillas2010
copyright©amberpasillas2010
Perimeter – (P) The distance around a figure.
10 ft. 10 ft.
10 ft.
6 ft.
106
1010+
36 ft.
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PERIMETER: Is the distance around a figure.
When you add the sides you are adding the units.
When you add units, your units DO NOT CHANGE!
If this rectangle has units in inches, then you are adding in + in + in + in = in
You must include units in every answer!
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The Area of a figure is the number of square units needed to cover it.
A = 2 • 3
A = 6 square units
A = 6 units2 2
3
PERIMETER: Is the distance around a figure.
in + in + in + in = in
AREA: Is the square units that cover a figure.
length • width= in • in = in2
VOLUME: The number of cubic units inside a figure.
length • width • height in • in • in = in3
length
length width
height
squared
cubed
width
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copyright©amberpasillas2010
8 m
6 m
A = 8 • 62
= 24 m2
A = base • height 2
A triangle is half the area of a rectangle. To find the area of a triangle you use the rectangle formula and divide it in half.
bhA=
2
5 m
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5 in
3 inA = b • h
A = 5 • 3 = 15 in2
To find the area for a parallelogram use what you know about area of a rectangle.
A = base • height4 in
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6 ft
3 ft
A = (b1 + b2) • h2
4 ft
A = (3 + 6) • 42A = (9) • 4
2= 36
2 = 18 ft2
A = (base1 + base2) • height
25 ft
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Take out your STUDY GUIDE
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Perimeter & Area Review
# 11
The Area (A) of a figure is the number of square units needed to cover it.
The Perimeter (P) is the distance around a figure.
a
b
c P= a+b+c units
height
base
(h)(b)
A = 2 • 6
12 square units 12 units2
9 cm
5 cm 6 cm3 cm
Area & Perimeter of a Triangle
# 12
PerimeterP = a + b + c
P = 5 + 6 + 9
P = 20 cm
Area1A b h2
1A 9 32
1A 272
2A 13.5 cm
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copyright©amberpasillas2010
#13 Perimeter & Area of a Rectangle The Perimeter of a figure is the distance around a figure.
2 in. 2 in.
5 in.
5 in.
2525+
14 in.
2 2P l w
The Area of a figure is the number of square units needed to cover it.
A = 3 • 2
6 square units
6 units2
A b h 3
2
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Teacher Note: The following study guide slides were taken from the lesson on Perimeter and Area review under the PERIMETER FOLDER
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a
b
c
de
f
g
h P=a+b+c+d+e+f+g+h
a
b
cP= a+b+c
P=4ss
s
s
s
l
l
w w
P=2l+2w
#9
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#10 Perimeter of a TrianglePerimeter: Distance around a geometric figure.
a 3 cm
c 7 cm
b 5 cm
P a b c
P 15 cmP 3 5 7
When you add thesides, you are alsoadding the units. When you add units,your UNITS DO NOTCHANGE!
You must include units in every answer!
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#11 Perimeter of a Rectangle & SquareThe Perimeter of a figure is the distance around a figure.
2 in. 2 in.
5 in.
5 in.
2525+
14 in.
Rectangle
45
2 2P l w
2(5) 2(4)P
18 units
4P s8 ft
8 ft
4(8)P 32 ft
Square
10 8
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Teacher Note: Extra lesson on just area
formulas without the perimeter
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Area of a RectangleArea of a Square
Area of a Triangle
Area of a Parallelogram
Area of a Trapezoid
REVIEW OF FORMULAS
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Area of a Rectangle
height
base
(h)
(b)
A = bh
The area of this rectangle is 8 squares, or 8 units squared
Area is in units2 because you are multiplying units.
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A square is a special rectangle
Since the base and the height are the same size, we call them sides (s) instead of base and height.
sheight = s
s base = s
A= s2
Area of a Square
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What is the area of the square?
4 m.
4 m.
44x
16 m.2
16 m2 or square meters
Area of a Square
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Area of a TriangleGiven the formula for
area of a rectangle, we are going to use that information to
discover the formula for the area of a triangle.
Watch carefully not to miss it!
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Area of a TriangleGiven a right triangle
Make a similar triangle,
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Area of a TriangleGiven a right triangle
Make a similar triangle, flip it and put both triangles next to each other
What polygon is this?
A Rectangle
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Area of a Triangle
What is the formula for the area of a triangle?
We can use the formula for area of a rectangle to find the formula for area of a triangle.
bA=
2
hA=b h
Two triangles make one rectangle.
We want to find half of the area of the rectangle.
We since we are
finding of the area.
÷2
half
base
height
b
h
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Area of a Triangle
base
heighth
This holds true for any triangle
b hA=
2
Notice when we put two right triangles together
it made a rectangle. When we put two isosceles
triangles together it made a parallelogram.
We are still finding half the area so we divide by 2.
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Draw a straight line from the top corner perpendicular to the base
Cut that triangle and move it to the other sideWhat shape does it make?
Rectangle
Area for a Parallelogram
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What is the formula for area of a parallelogram?
A parallelogram has the same area as a rectangle
h
base = b
height = h h
b
A=b h
Area for a Parallelogram
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4 cm.90º
2 cm.
= 8 cm.2
Check to see if you got it right.
A=b h
A=4 2
Area for a Parallelogram
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4 cm.90º
2 cm.
= 8 cm.2
A=b h
A=4 2
Cut off the piece at the dotted line.
Area for a Parallelogram
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4 cm.90º
2 cm.
= 8 cm.2
A=b h
A=4 2
Cut off the piece at the dotted line.
Area for a Parallelogram
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4 cm.90º
2 cm.
= 8 cm.2
A=b h
A=4 2
Move this piece to the other side.
Area for a Parallelogram
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4 cm.90º
2 cm.
= 8 cm.2
A=b h
A=4 2
Move this piece to the other side.
Area for a Parallelogram
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4 cm.90º
2 cm.
= 8 cm.2
A=b h
A=4 2
Now you have a rectangle
A = 8 square cm. or 8 cm.2
Let’s check it with the area of a rectangle.
How many squares do you see?
Area for a Parallelogram
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b1
b2
h
Copy that trapezoid, flip it over, and put it next to the original
b1
b2
h
Given the height, base 1, and base 2
(b1 + b2)
h
What shape is it now?
Parallelogram
Area of a Trapezoid
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Notice that the trapezoid is half the area of the parallelogram. It takes two trapezoids to make one parallelogram.
(b1 + b2)
h
Given our original trapezoid Put together with a similar flipped trapezoid, we found it made a parallelogram.
We are going to use the area of a parallelogram to find the area of a trapezoid.
Area of a Trapezoid
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(b1 + b2)
h
Parallelogram Trapezoid
A = (b1 + b2)
2
A=b h h
Area of a Trapezoid
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Area of Trapezoid
A = (b1 + b2) 2
2 in
6 in
3 in
= 12 in2
h
(2 6) 3A
2
(8) 3
2
24
2
Area of a Trapezoid
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Area of a Trapezoid
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