find the area of the figure. (sides meet at right angles.)

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{ "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 Rectangles" ], "new_concepts": [], "current_concepts": [ "Area of Composite Figures", "Area of Rectangles" ] } ## Decompose the composite figure into two rectangles $$ \begin{aligned} &\text{Total Width} = 8\text{ ft}\ &\text{Bottom Right Width} = 4\text{ ft}\ &\text{Bottom Left Width} = 8 - 4 = 4\text{ ft}\ &\text{Total Height} = 7\text{ ft}\ &\text{Bottom Cutout Height} = 2\text{ ft}\ &\text{Left Side Height} = 7 - 2 = 5\text{ ft} \end{aligned} $$ ## Calculate the area of each decomposed rectangle $$ \begin{aligned} &\text{Area of Left Rectangle} = 4\text{ ft} \times 5\text{ ft} = 20\text{ ft}^2\ &\text{Area of Right Rectangle} = 4\text{ ft} \times 7\text{ ft} = 28\text{ ft}^2 \end{aligned} $$ ## Sum the areas to find the total area $$ \text{Total Area} = 20\text{ ft}^2 + 28\text{ ft}^2 = 48\text{ ft}^2 $$ Find the area of the figure. (Sides meet at right angles.) 48 $\text{ft}^2$ { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Geometry", "Area of Composite Figures" ] }

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Question

Explanation:

Decompose the composite figure into two rectangles

Calculate the area of each decomposed rectangle

Sum the areas to find the total area

Answer: