a blueprint of sarahs room and walk-in closet is represented below. each box on the diagram represents 1 square foot. how much carpet would sarah need to cover the entire space?

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Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Coordinate Geometry" ], "new_concepts": [ "Area of Composite Figures" ], "current_concepts": [ "Coordinate Geometry", "Area of Composite Figures" ] } ## Divide the composite figure into two rectangles $$ \begin{aligned} &\text{Rectangle 1 (Left): } x \in [-5, 4], \quad y \in [2, 6] \ &\text{Rectangle 2 (Right): } x \in [4, 7], \quad y \in [-2, 6] \end{aligned} $$ ## Calculate the area of each rectangle $$ \begin{aligned} &\text{Width}_1 = 4 - (-5) = 9, \quad \text{Height}_1 = 6 - 2 = 4 \ &\text{Area}_1 = 9 \times 4 = 36 \ &\text{Width}_2 = 7 - 4 = 3, \quad \text{Height}_2 = 6 - (-2) = 8 \ &\text{Area}_2 = 3 \times 8 = 24 \end{aligned} $$ ## Sum the areas to find the total area $$ \text{Total Area} = \text{Area}_1 + \text{Area}_2 = 36 + 24 = 60 $$ 60 square feet { "subject": "Mathematics", "question_type": "Free Response", "knowledge_point": [ "Mathematics", "Geometry", "Area of Composite Figures" ] }

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Explanation:

Divide the composite figure into two rectangles

Calculate the area of each rectangle

Sum the areas to find the total area

Answer: