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

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{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": true, "concepts_used": [ "Area of Trapezoid", "Perimeter of Trapezoid", "Unit Conversion" ], "new_concepts": [], "current_concepts": [ "Area of Trapezoid", "Perimeter of Trapezoid", "Unit Conversion" ] } ## Convert height units to inches Using the *Unit Conversion* knowledge point $$ \begin{aligned} h &= \frac{2}{3}\text{ ft}\ h &= \frac{2}{3} \times 12\text{ in}\ h &= 8\text{ in} \end{aligned} $$ ## Calculate the area of the trapezoid Using the *Area of Trapezoid* knowledge point $$ \begin{aligned} A &= \frac{1}{2}(b_1 + b_2)h\ A &= \frac{1}{2}(18 + 6) \times 8\ A &= \frac{1}{2}(24) \times 8 = 96\text{ in}^2 \end{aligned} $$ ## Calculate the perimeter of the trapezoid Using the *Perimeter of Trapezoid* knowledge point $$ \begin{aligned} P &= b_1 + b_2 + s_1 + s_2\ P &= 18 + 6 + 10 + 10\ P &= 44\text{ in} \end{aligned} $$ (a) The area of the quadrilateral is 96 square inches ($\text{in}^2$). (b) The perimeter of the quadrilateral is 44 inches ($\text{in}$). { "elements": [ { "type": "polygon", "params": [ [-3, -2], [6, -2], [3, 2], [0, 2] ], "properties": { "strokeColor": "#8C55F2", "fillColor": "rgba(140, 85, 242, 0.15)", "strokeWidth": 2 } }, { "type": "segment", "params": [ [0, 2], [0, -2] ], "properties": { "strokeColor": "#583C87", "strokeWidth": 1.5, "dash": 2 } }, { "type": "segment", "params": [ [0, -1.7], [0.3, -1.7] ], "properties": { "strokeColor": "#583C87", "strokeWidth": 1 } }, { "type": "segment", "params": [ [0.3, -1.7], [0.3, -2] ], "properties": { "strokeColor": "#583C87", "strokeWidth": 1 } }, { "type": "text", "params": [ 1.5, 2.3, "6 in" ], "properties": { "color": "#583C87" } }, { "type": "text", "params": [ 1.5, -2.4, "18 in" ], "properties": { "color": "#583C87" } }, { "type": "text", "params": [ -2.2, 0.2, "10 in" ], "properties": { "color": "#583C87" } }, { "type": "text", "params": [ 5.0, 0.2, "10 in" ], "properties": { "color": "#583C87" } }, { "type": "text", "params": [ 0.2, 0, "\frac{2}{3} \text{ ft}" ], "properties": { "color": "#583C87" } } ] } { "subject": "Mathematics", "question_type": "Free Response", "knowledge_point": [ "Mathematics", "Geometry", "Area of Trapezoid" ] }

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Explanation:

Convert height units to inches

Calculate the area of the trapezoid

Calculate the perimeter of the trapezoid

Answer: