area of a parallelogram


Today we are going to find the Area of Parallelograms and

the Area of Triangles


AreaThe number of square units that are needed to cover the surface of a figure.

PolygonAny straight-sided closed plane figure.


Circle the polygons below.

Regular Polygon Polygon with all sides congruent and all angles congruent.


Polygons Regular PolygonsName# of sides Picture NamePicture

3 Triangle AcuteEquilateral

4 Quadrilateral Square

5 Pentagon RegularPentagon

6 Hexagon RegularHexagon


Polygons Regular PolygonsName# of sides Picture NamePicture

8 Octagon RegularOctagon

10 Decagon RegularDecagon

7 Heptagon

9 Nonagon


The area of a rectangle is equal to the base times the height. Also known as length times width.

height

base

(h)

(b)

A =bh

A = bh is the same as A = lw


What is the area of the rectangle?

2 in.

6 in.

26x

12 in.2

12 in2 or square inches


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


What is the area of the square?

4 m.

4 m.

44x

16 m.2

16 m2 or square meters


Given the formula for area of a rectangle, we are

going to use that information to derive the formula for the area of a parallelogramWatch carefully not to

miss it!


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


What is the formula for area of a parallelogram?

Use this information to find the area of a parallelogram

A parallelogram has the same area as a rectangle!

h

base = b

height = h h

b

A=b h


4 cm.90º

2 cm.

= 8 cm.2

Check to see if you got it right.

A=b h

A=4 2


4 cm.90º

2 cm.

= 8 cm.2

A=b h

A=4 2

Cut off the piece at the dotted line.


4 cm.90º

2 cm.

= 8 cm.2

A=b h

A=4 2

Move this piece to the other side.


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?


What is the area of this parallelogram?

7 cm.

5 cm. 57x

35 cm.2

35 square centimeters or 35 cm.2


What is the area of this parallelogram?

6 ft.

5 ft.56x

30 ft.2

30 square feet or 30 ft.2


Given 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!


Given a right triangle

Make a similar triangle,


Given a right triangle

Make a similar triangle, flip it and put both triangles next to each other

What polygon is this?

A Rectangle


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=2hA=b h

Two triangles make one rectangle.

We want to find half of the area of the rectangle.

We since we arefinding of the area.

÷2half

base

height

b

h


When we put 2 right triangles together is made a rectangle.Watch what happens when instead we use 2 isosceles triangles.


Given an isosceles triangle

Make a similar triangle,


Given an isosceles triangle

Make a similar triangle, flip it and put both triangles next to each other

What polygon is this?

A Parallelogram


base

height h

How do you find the area of the parallelogram?

Notice when we put two right triangles togetherit made a . When we put two isosceles triangles together it made a . We are still finding the area so we .half

rectangleparallelogr

dividea

by 2m

A= 12

bhbhA=2


9 cm

5 cm 6 cm3 cm

A= 12

bhbhA=2

1A b h2

1A 9 32

1A 272

2A 13.5 cm


The End!Take out your study guide!


Area of a Parallelogram

# 3

5 in

3 in A = b x hA = 5 x 3 = 15 in2

To find the area for a parallelogram use what you know about area of a rectangle.

A = base x height


# 4 Area of a Triangle

8 m

6 m

A = 8 x 62

= 24 m2

A = base x 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.

1A= bh2

bhA=2

area of a parallelogram

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