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{ "quality": "blurry", "question_count": 3, "skills_matched": [ "step_cot", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Square Properties", "Area of a Circle" ], "new_concepts": [ "Composite Area" ], "current_concepts": [ "Square Properties", "Area of a Circle", "Composite Area" ] } ## Calculate the total area of the square regions $$ \begin{aligned} &s = 6\text{ in.} \ &N_{\text{squares}} = 3 \ &A_{\text{squares}} = 3 \times s^2 = 3 \times 6^2 = 3 \times 36 = 108 \end{aligned} $$ ## Calculate the total area of the circular regions $$ \begin{aligned} &d = s = 6\text{ in.} \implies r = 3\text{ in.} \ &N_{\text{semicircles}} = 4 \implies N_{\text{circles}} = 2 \ &A_{\text{circles}} = 2 \times \pi r^2 = 2 \times \pi \times 3^2 = 18\pi \end{aligned} $$ ## Calculate the approximate total area of the figure $$ \begin{aligned} &\pi \approx 3.14 \ &A_{\text{total}} = 108 + 18 \times 3.14 = 108 + 56.52 = 164.52 \end{aligned} $$ ## Question 1 Each square has a side length of 6 in. What is the total area of the square regions? $A_{\text{squares}} =$ 108 $\text{in}^2$ ## Question 2 What is the total area of the circular regions? Write your answer using 'pi' with no spaces. $A_{\text{circles}} =$ 18pi $\text{in}^2$ ## Question 3 What is the approximate area of the figure? Use 3.14 for $\pi$. $A_{\text{total}} =$ 164.52 $\text{in}^2$ { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Geometry", "Composite Area" ] }

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Calculate the total area of the square regions

Calculate the total area of the circular regions

Calculate the approximate total area of the figure

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Question 1

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Question 3