Question

determine (a) the area and (b) the perimeter of the quadrilateral. note that the figure is not drawn to scale.

Explanation:

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<reasoning>

Convert the height unit to inches

Using the Unit Conversion knowledge point
\[

$$\begin{aligned} h &= 1\frac{1}{4}\text{ ft} = \frac{5}{4}\text{ ft}\\ h &= \frac{5}{4} \times 12\text{ in} = 15\text{ in} \end{aligned}$$

\]

Calculate the area of the trapezoid

Using the Area of Trapezoid knowledge point
\[

$$\begin{aligned} b_1 &= 8\text{ in},\quad b_2 = 16\text{ in},\quad h = 15\text{ in}\\ A &= \frac{1}{2}(b_1 + b_2)h\\ A &= \frac{1}{2}(8 + 16) \times 15 = \frac{1}{2}(24) \times 15 = 180\text{ in}^2 \end{aligned}$$

\]

Calculate the perimeter of the trapezoid

Using the Perimeter of Trapezoid knowledge point
\[

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

\]
</reasoning>

<answer>
(a) The area of the quadrilateral is 180 square inches (\(\text{in}^2\)).
(b) The perimeter of the quadrilateral is 34 inches (\(\text{in}\)).
</answer>

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"subject": "Mathematics",
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"Mathematics",
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"Area of Trapezoid"
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Answer:

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</pre_analysis>

<reasoning>

Convert the height unit to inches

Using the Unit Conversion knowledge point
\[

$$\begin{aligned} h &= 1\frac{1}{4}\text{ ft} = \frac{5}{4}\text{ ft}\\ h &= \frac{5}{4} \times 12\text{ in} = 15\text{ in} \end{aligned}$$

\]

Calculate the area of the trapezoid

Using the Area of Trapezoid knowledge point
\[

$$\begin{aligned} b_1 &= 8\text{ in},\quad b_2 = 16\text{ in},\quad h = 15\text{ in}\\ A &= \frac{1}{2}(b_1 + b_2)h\\ A &= \frac{1}{2}(8 + 16) \times 15 = \frac{1}{2}(24) \times 15 = 180\text{ in}^2 \end{aligned}$$

\]

Calculate the perimeter of the trapezoid

Using the Perimeter of Trapezoid knowledge point
\[

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

\]
</reasoning>

<answer>
(a) The area of the quadrilateral is 180 square inches (\(\text{in}^2\)).
(b) The perimeter of the quadrilateral is 34 inches (\(\text{in}\)).
</answer>

<post_analysis>
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"subject": "Mathematics",
"question_type": "Multi-part",
"knowledge_point": [
"Mathematics",
"Geometry",
"Area of Trapezoid"
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