find the area of a regular pentagon with an apothem of 6 inches and a side length of 8.7 inches.

? $\text{in}^2$

Question

find the area of a regular pentagon with an apothem of 6 inches and a side length of 8.7 inches.

?  $\text{in}^2$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Area of Regular Polygon", "Apothem" ], "new_concepts": [], "current_concepts": [ "Area of Regular Polygon", "Apothem", "Regular Polygon Properties" ] } ## Identify the given parameters Using the *Apothem* knowledge point $$ \begin{aligned} &n = 5\ &a = 6\text{ in}\ &s = 8.7\text{ in} \end{aligned} $$ ## Calculate the perimeter Using the *Area of Regular Polygon* knowledge point $$ \begin{aligned} &P = n \cdot s\ &P = 5 \cdot 8.7 = 43.5\text{ in} \end{aligned} $$ ## Calculate the area Using the *Area of Regular Polygon* knowledge point $$ \begin{aligned} &A = \frac{1}{2} \cdot P \cdot a\ &A = \frac{1}{2} \cdot 43.5 \cdot 6 = 130.5\text{ in}^2 \end{aligned} $$ Find the area of a regular pentagon with an apothem of 6 inches and a side length of 8.7 inches. 130.5 $\text{in}^2$ { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Geometry", "Area of Regular Polygon" ] }

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QUESTION IMAGE

Question

Explanation:

Identify the given parameters

Calculate the perimeter

Calculate the area

Answer: