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{ "quality": "blurry", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [], "new_concepts": [ "Area of Regular Hexagon", "Apothem of Hexagon" ], "current_concepts": [ "Area of Regular Hexagon", "Apothem of Hexagon", "Trigonometry in Polygons" ] } ## Calculate the area of a regular hexagon using the radius $$ \begin{aligned} &r = 4\text{ in.} \ &A = \frac{3\sqrt{3}}{2} r^2 \ &A = \frac{3\sqrt{3}}{2} (4)^2 = 24\sqrt{3}\text{ in.}^2 \end{aligned} $$ ## Approximate the numerical value $$ \begin{aligned} &\sqrt{3} \approx 1.732 \ &A \approx 24 \times 1.732 \approx 41.57\text{ in.}^2 \end{aligned} $$ ## Match with the closest option $$ A \approx 42\text{ in.}^2 $$

(A) $24\text{ in.}^2$

(B) $42\text{ in.}^2$

(C) $48\text{ in.}^2$

(D) $84\text{ in.}^2$

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Geometry", "Area of Regular Hexagon" ] }

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Question

Explanation:

Calculate the area of a regular hexagon using the radius

Approximate the numerical value

Match with the closest option

Answer: