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

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Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "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 $$ \begin{aligned} &\text{Total Width} = 15\text{ in}\ &\text{Top Rectangle Width} = 5\text{ in}\ &\text{Bottom Right Cutout Width} = 2\text{ in}\ &\text{Middle Section Width} = 15 - 5 - 2 = 8\text{ in}\ &\text{Top Rectangle Height} = 6\text{ in}\ &\text{Bottom Right Section Height} = 6 - 2 = 4\text{ in}\ &\text{Triangle Base} = 15 - 5 = 10\text{ in}\ &\text{Triangle Height} = 6 - 2 = 4\text{ in} \end{aligned} $$ ## Calculate the area of each component $$ \begin{aligned} &\text{Area}_{\text{rectangle}} = 5 \times 6 = 30\text{ in}^2\ &\text{Area}_{\text{triangle}} = \frac{1}{2} \times 10 \times 4 = 20\text{ in}^2\ &\text{Area}_{\text{cutout}} = 2 \times 2 = 4\text{ in}^2 \end{aligned} $$ ## Calculate the total area of the figure $$ \begin{aligned} &\text{Area}_{\text{total}} = \text{Area}_{\text{rectangle}} + \text{Area}_{\text{triangle}} - \text{Area}_{\text{cutout}}\ &\text{Area}_{\text{total}} = 30 + 20 - 4 = 46\text{ in}^2 \end{aligned} $$ What is the area of this figure? 46 square inches { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Geometry", "Area of Composite Figures" ] }

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Explanation:

Decompose the composite figure into simpler shapes

Calculate the area of each component

Calculate the total area of the figure

Answer: