Find the area of trapezoid ABCD by decomposing it into a rectangle and triangle.
Responses
A 80
80 cm 2
B 96
96 cm 2
C 104
104 cm 2
D 112
112 cm 2
B 96 cm^2
To find the area of the trapezoid, we can decompose it into a rectangle and triangle.
The height of the trapezoid is 8 cm, and the top base AD is 10 cm, while the bottom base BC is 14 cm.
First, calculate the area of the rectangle: Area = Base x Height = 14 cm x 8 cm = 112 cm^2
Next, calculate the area of the triangle on top: Area = 1/2 x Base x Height = 1/2 x (14 cm - 10 cm) x 8 cm = 1/2 x 4 cm x 8 cm = 16 cm^2
Add the area of the rectangle and the triangle together: Area = 112 cm^2 (rectangle) + 16 cm^2 (triangle) = 128 cm^2
However, the area of the trapezoid is half of the above value because it is decomposed into a rectangle and a triangle: 128 cm^2 / 2 = 64 cm^2
Therefore, the correct answer is B. 96 cm^2.