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 area formula for trapezoid

The formula for the area 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: Substitute given values

We know that $A = 70.55$ square - feet, $b_1=11.4$ feet, and $b_2 = 5.6$ feet. Substituting into the formula gives $70.55=\frac{(11.4 + 5.6)h}{2}$.

Step3: Simplify the base - sum

First, calculate $b_1 + b_2$: $11.4+5.6 = 17$ feet. So the equation becomes $70.55=\frac{17h}{2}$.

Step4: Solve for h

Multiply both sides of the equation by 2 to get $70.55\times2=17h$, which simplifies to $141.1 = 17h$. Then divide both sides by 17: $h=\frac{141.1}{17}=8.3$ feet.

Answer:

C. 8.3 ft