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Question

A manufacturing plant is designed to be in the shape of a regular pentagon with 92.5 ft on each side. A security fence surrounds the building to form a circle, and each corner of the building is to be 25.0 ft from the closest point on the fence. How much fencing is required?

Solution

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1 of 3The radii of the circular fencing divides the pentagon into six congruent isosceles triangles. The bases of the triangles are 92.5 ft since the sides of the pentagon are 92.5 ft. Let $d$ be the congruent sides of the isosceles triangles. The vertex angle of each triangle is $\dfrac{360\text{\textdegree}}{5}=72\text{\textdegree}$. The altitude of each isosceles triangle bisects the vertex angle and base as shown in the figure on the right.

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