EXAMPLE 2.6.14 solution

The diagram below shows the courtyard at the Institute for Wolverine Studies. The shaded area represents lawn, while the circular area is a pool. Gomer has a contract to mow the lawn. He charges $0.02 per square foot for this service. Find the total cost for this job (he will mow the lawn, but not the pool).

We need to find the area of region to mowed (in square feet) and multiply by the cost factor of $0.02 per square foot.

The area of the region to be mowed is equal to the area of the rectangle minus the area of the circular pool:

Area to be mowed = (100) times (100) minus pi times (25 squared)

= 10,000 minus 1963.5 = 8036.5 square feet

Cost = (8036.5 square feet) times ($0.02 per square foot) = $160.73