Question

1. the area of a trapezoid is 84 ft². the bases are 4 ft and 20 ft. find the height.
2. the area of a trapezoid is 60 m². the bases are 8 m and 16 m. find the height.

Explanation:

Step1: Recall area formula

The area formula of a trapezoid is $A=\frac{(b_1 + b_2)h}{2}$, where $A$ is the area, $b_1$ and $b_2$ are the bases, and $h$ is the height.

Step2: Rearrange formula for height

We can rewrite the formula for $h$ as $h=\frac{2A}{b_1 + b_2}$.

Step3: Solve for question 7

Given $A = 84$ ft², $b_1=4$ ft, $b_2 = 20$ ft. Substitute into the formula: $h=\frac{2\times84}{4 + 20}=\frac{168}{24}=7$ ft.

Step4: Solve for question 8

Given $A = 60$ m², $b_1=8$ m, $b_2 = 16$ m. Substitute into the formula: $h=\frac{2\times60}{8 + 16}=\frac{120}{24}=5$ m.

Answer:

1. 7 ft
2. 5 m