Copyright©amberpasillas2010. Today we are going to review Area of a Triangle & Parallelogram. Then...


Today we are going to review Area of a Triangle &

Parallelogram.

Then we are going to discover the Area of a Trapezoid.


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=

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


base

heighth

This holds true for any triangle

b hA=

2

Notice when we put two right triangles together

it made a . When we put two isosceles

triangles together it made a .

We are still finding the area so we .half

rectangle

parallelogr

divide

a

by 2

m


A triangle is half the area of a rectangle. To find the area of a triangle, you use the rectangle formula (base times height) and divide it in half. A = base • height

2

5 m

12 m13 m

A = 5 • 122 = 30 m2

A=1

2bh

bhA=

2


11 cm

5 cm 8 cm

Perimeter

Area

P = a + b + c

1A b h2

P = 5 + 8 + 11P = 24 cm

3 cm

1A 11 32

1A 332

2A 16.5 cm

Find the perimeter and area of this triangle.


Given the formula for area of a triangle and the

formula for area of a parallelogram we are going to

use that information to discover the formula for the area of a

trapezoidWatch carefully not to miss it!


This trapezoid is regular. regular trapezoid

This trapezoid is an irregular trapezoid.

irregular trapezoid

Also known as an isosceles trapezoid


b2

b1

h

Copy that trapezoid, flip it over, and put it next to the original

b2

b1

h

Give the height, base 1 & base 2

(b1 + b2)

h

What polygon is it now?

Parallelogram


Notice that the trapezoid is half the area of the 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. It takes two trapezoids to make one parallelogram.


(b1 + b2)

h

Parallelogram

Trapezoid

A = b h

Notice that the trapezoid is half the area of the parallelogram.How do we find

half the area?

2

A = (b1 + b2) • h

Hint: Think of area of a triangle.


Area of Trapezoid

2 in

6 in

3 in

A (2 6) (8) 3

2

24

2 = 12 in2

2

A = (b1 + b2) • h

3

2

4 in


Area of Trapezoid

3 m

8 m

4 m

A (3 8) (11) 4

2

44

2 = 22 m2

2

A = (b1 + b2) • h

4

2

5 m


4 in

5 in

7 in

6 in

1A (5 7) 4

2

1 2

1A (b b ) h

2

1A (12) 4

2

A 6 4 224 in

Here is another way to look at the trapezoid formula.

Instead of dividing by 2, multiply by ½


The End!Take out your study guide!


# 5 Area of a Trapezoid

5 ft

4 ft

A = (b1 + b2) x h2

3 ft

A = (4 + 5) x 32

A = (9) x 3 2

272 = 13.5 ft2

A = (base1 + base2) x height 2

=


Area of Polygons#6

The Area of a figure is the number of square units needed to cover it.

Rectangle

45

A l w

A 5 4

A un20 2

A b h

1078

A 10 7

A un70 2

Parallelogram Triangle

58

8 5A

2

A un20 2

7 b•hA=

2

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