Question

8 in.
5 in.
\frac{1}{4} ft
5 in.
16 in.

Explanation:

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<reasoning>

Convert height units to inches

Using the Unit Conversion knowledge point
\[

$$\begin{aligned} h &= \frac{1}{4}\text{ ft}\\ h &= \frac{1}{4} \times 12\text{ in.}\\ h &= 3\text{ in.} \end{aligned}$$

\]

Calculate the area of the trapezoid

Using the Area of Trapezoid knowledge point
\[

$$\begin{aligned} A &= \frac{1}{2} \times (b_1 + b_2) \times h\\ A &= \frac{1}{2} \times (8\text{ in.} + 16\text{ in.}) \times 3\text{ in.}\\ A &= \frac{1}{2} \times 24\text{ in.} \times 3\text{ in.}\\ A &= 36\text{ sq in.} \end{aligned}$$

\]

Calculate the perimeter of the trapezoid

Using the Perimeter of Trapezoid knowledge point
\[

$$\begin{aligned} P &= \text{sum of all outer sides}\\ P &= 8\text{ in.} + 5\text{ in.} + 16\text{ in.} + 5\text{ in.}\\ P &= 34\text{ in.} \end{aligned}$$

\]
</reasoning>

<answer>
The area of the trapezoid is 36 square inches (\(\text{in}^2\)) and the perimeter is 34 inches (\(\text{in.}\)).
</answer>

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Answer:

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<reasoning>

Convert height units to inches

Using the Unit Conversion knowledge point
\[

$$\begin{aligned} h &= \frac{1}{4}\text{ ft}\\ h &= \frac{1}{4} \times 12\text{ in.}\\ h &= 3\text{ in.} \end{aligned}$$

\]

Calculate the area of the trapezoid

Using the Area of Trapezoid knowledge point
\[

$$\begin{aligned} A &= \frac{1}{2} \times (b_1 + b_2) \times h\\ A &= \frac{1}{2} \times (8\text{ in.} + 16\text{ in.}) \times 3\text{ in.}\\ A &= \frac{1}{2} \times 24\text{ in.} \times 3\text{ in.}\\ A &= 36\text{ sq in.} \end{aligned}$$

\]

Calculate the perimeter of the trapezoid

Using the Perimeter of Trapezoid knowledge point
\[

$$\begin{aligned} P &= \text{sum of all outer sides}\\ P &= 8\text{ in.} + 5\text{ in.} + 16\text{ in.} + 5\text{ in.}\\ P &= 34\text{ in.} \end{aligned}$$

\]
</reasoning>

<answer>
The area of the trapezoid is 36 square inches (\(\text{in}^2\)) and the perimeter is 34 inches (\(\text{in.}\)).
</answer>

<post_analysis>
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