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

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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": [], "new_concepts": [ "Area of Composite Figures", "Area of Triangles", "Area of Rectangles" ], "current_concepts": [ "Area of Composite Figures", "Area of Triangles", "Area of Rectangles" ] } ## Decompose the composite figure into simpler shapes $$ \begin{aligned} &\text{Shape 1 (Left Rectangle): } \text{width} = 5\text{ yd}, \text{ height} = 9\text{ yd} \ &\text{Shape 2 (Middle Rectangle): } \text{width} = 4\text{ yd}, \text{ height} = 9 - 4 = 5\text{ yd} \ &\text{Shape 3 (Right Triangle): } \text{base} = 5 + 4 + 6 - 5 = 10\text{ yd}, \text{ height} = 7\text{ yd} \end{aligned} $$ ## Calculate the area of each component $$ \begin{aligned} &\text{Area}_1 = 5 \times 9 = 45\text{ yd}^2 \ &\text{Area}_2 = 4 \times 5 = 20\text{ yd}^2 \ &\text{Area}_3 = \frac{1}{2} \times 10 \times 7 = 35\text{ yd}^2 \end{aligned} $$ ## Sum the areas to find the total area $$ \text{Total Area} = 45 + 20 + 35 = 100\text{ yd}^2 $$ What is the area of this figure? Write your answer using decimals, if necessary. 100 square yards { "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 simpler shapes

Calculate the area of each component

Sum the areas to find the total area

Answer: