Try the fastest way to create flashcards
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

Verified
Step 1
1 of 3

The 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.

## Recommended textbook solutions

#### Basic Technical Mathematics with Calculus

10th EditionISBN: 9780133253528Allyn J. Washington
12,707 solutions

#### Thomas' Calculus

14th EditionISBN: 9780134438986 (11 more)Christopher E Heil, Joel R. Hass, Maurice D. Weir
10,142 solutions

#### Calculus: Early Transcendentals

8th EditionISBN: 9781285741550 (4 more)James Stewart
11,085 solutions

#### Calculus: Early Transcendentals

9th EditionISBN: 9781337613927 (1 more)Daniel K. Clegg, James Stewart, Saleem Watson
11,049 solutions