This lesson will show you how we find the area of a trapezoid using two different methods.
The first method will help you see why the formula for finding the area of trapezoids work. Let us get started! Cut the trapezoid in three pieces and
make a rectangle and a triangle with the pieces.
Then, we need to make the following four important observations.
1.
Rectangle
Base = 4
Height = 8
2.
Trapezoid
Length of bottom base = 13
Length of top base = 4
Height = 8
3.
Newly formed triangle (made with blue and orange lines)
Length of base = 9 = 13 - 4 = length of bottom base of trapezoid - 4
Height = 8
4.
Area of trapezoid = area of rectangle + area of newly formed triangle.
Now our strategy will be to compute the area of the rectangle and the area of the newly formed triangle and see if we can make the formula for finding the area of trapezoid magically appear.
Area of rectangle = base × height = 4 × 8
Area of triangle = ( base × height ) / 2
Area of triangle = [(13 - 4) × 8 ] / 2 = [13 × 8 + - 4 × 8] / 2
Area of triangle = (13 × 8) / 2 + (- 4 × 8) / 2
Area of trapezoid = 4 × 8 + (13 × 8) / 2 + (- 4 × 8) / 2
Area of trapezoid = 8 × (4 + 13 / 2 + - 4 / 2)
Area of trapezoid = 8 × (4 - 4 / 2 + 13 / 2)
Area of trapezoid = 8 × (8 / 2 - 4 / 2 + 13 / 2)
Area of trapezoid = 8 × (4 / 2 + 13 / 2)
Area of trapezoid = (4 / 2 + 13 / 2) × 8
Area of trapezoid = 1 / 2 × (4 + 13 ) × 8
Let b_{1} = 4 let b_{2} = 13, and let h = 8
Then, the formula to get the area of trapezoid is equal to 1 / 2 × (b_{1} + b_{2} ) × h
In general, if b_{1} and b_{2} are the bases of a trapezoid and h the height of the trapezoid, then we can use the formula below.
Example #1:
If b_{1} = 7 cm, b_{2} = 21 cm, and h = 2 cm, find A
Area = 1 / 2 × (b_{1} + b_{2} ) × h = 1 / 2 × (7 + 21) × 2 = 1 / 2 × (28) × 2
Area = 1 / 2 × 56 = 28 cm^{2}
Example #2:
If b_{1} = 15 cm, b_{2} = 25 cm, and h = 10 cm, find A
Area = 1 / 2 × (b_{1} + b_{2} ) × h = 1 / 2 × (15 + 25) × 10 = 1 / 2 × (40) × 10
Area = 1 / 2 × 400 = 200 cm^{2}
Example #3:
If b_{1} = 9 cm, b_{2} = 15 cm, and h = 2 cm, find A
Area = 1 / 2 × (b_{1} + b_{2} ) × h = 1 / 2 × (9 + 15) × 2 = 1 / 2 × (24) × 2
Area = 1 / 2 × 48 = 24 cm^{2}
Sep 17, 20 03:57 PM
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