each square has a side length of 4 in.
what is the total area of the square regions?
$a_{\text{squares}} = $ $\text{in}^2$
what is the total area of the circular regions? write your answer using $\pi$ with no spaces.
$a_{\text{circles}} = $ $\text{in}^2$
what is the approximate area of the figure? use 3.14 for $\pi$.
$a_{\text{total}} \approx $ $\text{in}^2$

Question

each square has a side length of 4 in.
what is the total area of the square regions?
$a_{\text{squares}} = $   $\text{in}^2$
what is the total area of the circular regions? write your answer using $\pi$ with no spaces.
$a_{\text{circles}} = $   $\text{in}^2$
what is the approximate area of the figure? use 3.14 for $\pi$.
$a_{\text{total}} \approx $   $\text{in}^2$

Accepted Answer

{ "quality": "clear", "question_count": 3, "skills_matched": [ "step_cot", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Square Properties", "Area of a Circle", "Composite Area" ], "new_concepts": [], "current_concepts": [ "Square Properties", "Area of a Circle", "Composite Area" ] } ## Calculate the total area of the square regions $$ \begin{aligned} s &= 4\text{ in} \ A_{\text{one square}} &= s^2 = 4^2 = 16\text{ in}^2 \ N_{\text{squares}} &= 3 \ A_{\text{squares}} &= 3 \times 16 = 48\text{ in}^2 \end{aligned} $$ ## Calculate the total area of the circular regions $$ \begin{aligned} d &= s = 4\text{ in} \ r &= \frac{d}{2} = 2\text{ in} \ A_{\text{one semicircle}} &= \frac{1}{2}\pi r^2 = \frac{1}{2}\pi (2)^2 = 2\pi\text{ in}^2 \ N_{\text{semicircles}} &= 5 \ A_{\text{circles}} &= 5 \times 2\pi = 10\pi\text{ in}^2 \end{aligned} $$ ## Calculate the approximate total area of the figure $$ \begin{aligned} \pi &\approx 3.14 \ A_{\text{circles}} &\approx 10 \times 3.14 = 31.4\text{ in}^2 \ A_{\text{total}} &= A_{\text{squares}} + A_{\text{circles}} \ A_{\text{total}} &\approx 48 + 31.4 = 79.4\text{ in}^2 \end{aligned} $$ ## Question 1 Each square has a side length of 4 in. What is the total area of the square regions? $A_{\text{squares}} =$ 48 $\text{in}^2$ ## Question 2 What is the total area of the circular regions? Write your answer using $\pi$ with no spaces. $A_{\text{circles}} =$ $10\pi$ $\text{in}^2$ ## Question 3 What is the approximate area of the figure? Use 3.14 for $\pi$. $A_{\text{total}} \approx$ 79.4 $\text{in}^2$ { "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

Question 2

Question 3