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What is the area of a regular decagon with a perimeter of 205 cm?
Wiki User
∙ 6y ago
The regular decagon will have 10 equal sides of 20.5 cm and consist of 10 isosceles triangles having 2 equal sides of 33.16969677 cm found by using the sine rule with equal base angles of 72 degrees and an apex angle of 36 degrees. Area: 0.5*33.16969677 squared *sin(36)*10 = 3233.491266 square cm
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The area of a regular polygon with a side length S and number of sides N can be found using the formula:
area = S² × ¼ × N ÷ tan(180° ÷ N)
For a regular decagon with a perimeter of 205 cm
S = 205 cm ÷ 10 = 20.5 cm
N = 10
→ area = (20.5 cm)² × ¼ × 10 ÷ tan(180° ÷ 10) ≈ 3233 cm²
Wiki User
∙ 6y ago
Wiki User
∙ 6y agoIt is 3233.5 cm2.
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