Question

find the area of trapezoid bcde. round your answer to the nearest tenth if necessary.

Explanation:

Step1: Recall trapezoid area formula

The area of a trapezoid is given by $\text{Area} = \frac{1}{2} \times (b_1 + b_2) \times h$, where $b_1$ and $b_2$ are the lengths of the two parallel sides, and $h$ is the height (perpendicular distance between the parallel sides).

Step2: Identify values for the formula

From the diagram, the parallel sides are $DC = 12.9$ in and the segment parallel to it (the side corresponding to $EB$'s parallel counterpart, but the two bases are $12.9$ in and the length we can infer as the other base: the side parallel to $DC$ is the side that, with the height 12.8 in, forms the trapezoid. Wait, no: the two parallel sides are $DC = 12.9$ in and the side $EB$ is not, actually the two parallel sides are $DE$ and $BC$? No, no, the height is 12.8 in, perpendicular to $BC$. The two parallel bases are $DC = 12.9$ in and the length of the side opposite, which is the length equal to... Wait, no, the trapezoid BCDE has parallel sides $DC$ and $EB$? No, the height is 12.8 in, which is the perpendicular distance between $DC$ and $EB$? No, the sides $DE = 9.6$ in, $BC = 19.2$ in, the two parallel sides are $DC$ and $EB$, with height 12.8 in. Wait, no, the formula is $\frac{1}{2} \times (\text{sum of the two parallel sides}) \times \text{height}$. The two parallel sides are $DC = 12.9$ in and $EB = 15.1$ in? No, no, the height is 12.8 in, which is the perpendicular distance between $DE$ and $BC$? Wait, no, the right angle is on $BC$, so the height is 12.8 in, between $DE$ and $BC$. So the two parallel sides are $DE = 9.6$ in and $BC = 19.2$ in, height $h = 12.8$ in.
Wait, no, trapezoid BCDE: vertices B, C, D, E. So sides BC, CD, DE, EB. So parallel sides are CD and EB? No, the perpendicular is to BC, so the parallel sides are DE and BC. Yes, that makes sense. So $b_1 = DE = 9.6$ in, $b_2 = BC = 19.2$ in, height $h = 12.8$ in.

Step3: Substitute values into formula

$\text{Area} = \frac{1}{2} \times (9.6 + 19.2) \times 12.8$
First calculate the sum inside the parentheses: $9.6 + 19.2 = 28.8$
Then multiply by the height: $28.8 \times 12.8 = 368.64$
Then multiply by $\frac{1}{2}$: $\frac{1}{2} \times 368.64 = 184.32$

Step4: Round to nearest tenth

$184.32$ rounded to the nearest tenth is $184.3$

Answer:

184.3 square inches