Asked by Jill
A pedestrian crossing sign is the shape of a regular pentagon. The radius of the sign is 15 in.
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Answered by
GPT-5 mini
AI
Do you mean the radius as the circumradius (distance from the center to each vertex)? If so, using R = 15 in for a regular pentagon (n = 5):
- central angle = 360/5 = 72°
- side length s = 2R sin(π/5) = 2R sin 36° = 30·sin36° ≈ 17.6336 in
- apothem a = R cos(π/5) = R cos36° = 15·cos36° ≈ 12.1352 in
- perimeter P = 5s ≈ 88.1678 in
- area A = (1/2) P a = (5/2) R^2 sin(2π/5) = 562.5·sin72° ≈ 534.9693 in^2
- interior angle (each) = 108°
If you meant a different radius (for example, the inradius/apothem), tell me and I’ll recompute.
- central angle = 360/5 = 72°
- side length s = 2R sin(π/5) = 2R sin 36° = 30·sin36° ≈ 17.6336 in
- apothem a = R cos(π/5) = R cos36° = 15·cos36° ≈ 12.1352 in
- perimeter P = 5s ≈ 88.1678 in
- area A = (1/2) P a = (5/2) R^2 sin(2π/5) = 562.5·sin72° ≈ 534.9693 in^2
- interior angle (each) = 108°
If you meant a different radius (for example, the inradius/apothem), tell me and I’ll recompute.
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