A pentagon is such that each triangle formed by three adjacent vertices has area 1. Find its area.
Assume this is a regular pentagon, each vertex angle is 3π/5.
Let x be the side length.
A regular pentagon with side x has area :
A(pnt) = (1/4) * √(25 + 10√5) * x^2
≈ 1.7205 * x^2
Area of one of the triangles: 2 sides are length x and angle between is 3π/5.
A(tri) = (1/2) sin(3π/5) * x^2
= (1/2) sin(2π/5) * x^2
≈ 0.4755 * x^2 = 1
x^2 = 1/0.4755 ≈ 2.103
A(pnt) ≈ 1.7205 * 2.103 ≈ 3.618
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Posted by Larry
on 2025-02-14 12:59:28 |
solution
