what is the area of this figure?
write your answer using decimals, if necessary.

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Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Area of Composite Figures", "Area of Triangles", "Area of Rectangles" ], "new_concepts": [], "current_concepts": [ "Area of Composite Figures", "Area of Triangles", "Area of Rectangles" ] } ## Decompose the composite figure into simpler shapes $$ \begin{aligned} &\text{Total Area} = \text{Area}_{\text{triangle}} + \text{Area}_{\text{rectangle, upper}} + \text{Area}_{\text{rectangle, lower}} - \text{Area}_{\text{cutout}} \end{aligned} $$ ## Calculate the area of each component $$ \begin{aligned} &\text{Width of main body} = 4 + 7 - 2 = 9\text{ km}\ &\text{Base of triangle} = 9 + 6 = 15\text{ km}\ &\text{Height of triangle} = 6\text{ km}\ &\text{Area}_{\text{triangle}} = \frac{1}{2} \times 15 \times 6 = 45\text{ km}^2\ &\text{Area}_{\text{main rectangle}} = 9 \times 8 = 72\text{ km}^2\ &\text{Area}_{\text{cutout}} = 2 \times 2 = 4\text{ km}^2 \end{aligned} $$ ## Sum the areas to find the total area $$ \begin{aligned} &\text{Total Area} = 45 + 72 - 4 = 113\text{ km}^2 \end{aligned} $$ $113\text{ km}^2$ { "subject": "Mathematics", "question_type": "Free Response", "knowledge_point": [ "Mathematics", "Geometry", "Area of Composite Figures" ] }

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Question

Explanation:

Decompose the composite figure into simpler shapes

Calculate the area of each component

Sum the areas to find the total area

Answer: