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Today we are going to review Area of a Triangle &
Parallelogram.
Then we are going to discover the Area of a Trapezoid.
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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!
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Given a right triangle
Make a similar triangle,
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Given 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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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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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
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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
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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.
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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!
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This trapezoid is regular.
regular trapezoid
This trapezoid is an irregular trapezoid.
irregular trapezoid
Also known as an isosceles trapezoid
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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
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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.
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(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.
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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
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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
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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
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The End!Take out your study guide!
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# 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
=
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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
