Question was provided via image upload.

Question

Accepted Answer

{ "quality": "blurry", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Area of Regular Hexagon", "Apothem of Hexagon", "Area of a Circle" ], "new_concepts": [], "current_concepts": [ "Area of Regular Hexagon", "Apothem of Hexagon", "Area of a Circle", "Composite Area" ] } ## Calculate the radius of the inscribed circle (apothem of the hexagon) $$ \begin{aligned} s &= 10\text{ ft} \ r &= a = \frac{s}{2}\sqrt{3} = \frac{10}{2}\sqrt{3} = 5\sqrt{3}\text{ ft} \end{aligned} $$ ## Calculate the area of the regular hexagon and the inscribed circle $$ \begin{aligned} A_{\text{hexagon}} &= \frac{3\sqrt{3}}{2}s^2 = \frac{3\sqrt{3}}{2}(10)^2 = 150\sqrt{3}\text{ ft}^2 \ A_{\text{circle}} &= \pi r^2 = \pi (5\sqrt{3})^2 = 75\pi\text{ ft}^2 \end{aligned} $$ ## Calculate the area of the shaded region $$ A_{\text{shaded}} = A_{\text{hexagon}} - A_{\text{circle}} = (150\sqrt{3} - 75\pi)\text{ ft}^2 $$

(A) $(150\sqrt{3} - 75\pi)\text{ ft}^2$

(B) $(300 - 75\pi)\text{ ft}^2$

(C) $(150\sqrt{3} - 25\pi)\text{ ft}^2$

(D) $(300 - 25\pi)\text{ ft}^2$

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Geometry", "Composite Area" ] }

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Calculate the radius of the inscribed circle (apothem of the hexagon)

Calculate the area of the regular hexagon and the inscribed circle

Calculate the area of the shaded region

Answer: