Question

the area of a trapezoid is 70.55 square feet. the length of the bases are 11.4 feet and 5.6 feet. what is the height of the trapezoid?
4.15 ft
4.15 ft²
8.3 ft
8.3 ft²

Explanation:

Step1: Recall trapezoid - 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 lengths of the bases, and $h$ is the height.

Step2: Rearrange the formula for height

We can rewrite the formula for $h$ as $h=\frac{2A}{b_1 + b_2}$. Given $A = 70.55$ square - feet, $b_1=11.4$ feet, and $b_2 = 5.6$ feet. First, find the sum of the bases: $b_1 + b_2=11.4+5.6 = 17$ feet.

Step3: Calculate the height

Then, substitute the values into the height formula: $h=\frac{2\times70.55}{17}=\frac{141.1}{17}=8.3$ feet.

Answer:

C. 8.3 ft