find the area of a regular decagon with an apothem of 5 meters and a side length of 3.25 meters.

? $\text{m}^2$

Question

find the area of a regular decagon with an apothem of 5 meters and a side length of 3.25 meters.

? $\text{m}^2$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "quick" ], "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 of the regular decagon $$ \begin{aligned} &n = 10 \quad \text{(number of sides for a decagon)}\ &a = 5\text{ m} \quad \text{(apothem)}\ &s = 3.25\text{ m} \quad \text{(side length)} \end{aligned} $$ ## Calculate the perimeter of the decagon $$ P = n \cdot s = 10 \cdot 3.25 = 32.5\text{ m} $$ ## Calculate the area of the regular decagon $$ A = \frac{1}{2} \cdot P \cdot a = \frac{1}{2} \cdot 32.5 \cdot 5 = 81.25\text{ m}^2 $$ Find the area of a regular decagon with an apothem of 5 meters and a side length of 3.25 meters. 81.25 $\text{m}^2$ { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Geometry", "Area of Regular Polygon" ] }

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Question

Explanation:

Identify the given parameters of the regular decagon

Calculate the perimeter of the decagon

Calculate the area of the regular decagon

Answer: