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

Question

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Unit Conversion", "Area of Trapezoid", "Perimeter of Trapezoid" ], "new_concepts": [], "current_concepts": [ "Unit Conversion", "Area of Trapezoid", "Perimeter of Trapezoid" ] } ## 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 $$ \begin{aligned} P &= \text{sum of all outer sides}\ P &= 8\text{ in.} + 5\text{ in.} + 16\text{ in.} + 5\text{ in.}\ P &= 34\text{ in.} \end{aligned} $$ The area of the trapezoid is 36 square inches ($\text{in}^2$) and the perimeter is 34 inches ($\text{in.}$). { "subject": "Mathematics", "question_type": "Free Response", "knowledge_point": [ "Mathematics", "Geometry", "Area of Trapezoid" ] }

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Question

Explanation:

Convert height units to inches

Calculate the area of the trapezoid

Calculate the perimeter of the trapezoid

Answer: