Chapter 11.4, Problem 4CYU

To determine

To find: the area of the pool.

Answer to Problem 4CYU

The Area of the pool is $109f{t}^2.$

Explanation of Solution

Given information: K's job is to cover the community pool during fall and winter.

Since the pool is in the shape of an octagon, needs to find the area in order to have a custom cover made.If the pool has the dimensions shown in the below figure

  

Calculation:

From the given figure, the area of the pool can be separated into eight right triangles with a hypotenuse of 6 ft., and base of the triangle measuring 5 ft., and height is $\sqrt{6^2-{(\frac{5}{2})}^2}=\sqrt{6^2-{(2.5)}^2}\approx 5.45ft.$ (By Pythagorean Theorem).

Area of the pool=8 $\times$ Area of the triangle.

= $8\times (\frac{1}{2}\times b\times h)=4\times 5\times 5.45=109f{t}^2.$

Therefore, the Area of the pool is $109f{t}^2.$