EXAMPLE 2.6.1

The diagram below shows the rectangular pen in which Gomer confines his wolverines and badgers. As a special treat, Gomer is going to cover the badgers' area of the pen with Astroturf. Assuming that Astroturf costs $1.25 per square foot, how much with this project cost? (Choose the closest answer.)

A. $1500 B. $9000

C. $4500 D. $3000

SOLUTION

To solve this problem we need to find the area of the triangular region (in square feet) and multiply by the cost factor of $1.25 per square foot.

The formula for the area of a triangle is illustrated below:

Now, in the figure shown the measurements are expressed in yards, but we want to compute the triangle's area in square feet, not square yards. This suggests that we should convert units from yards to feet before using the formula for area. To convert from yards to feet we multiply by 3:

Now we find the area, in square feet, of the triangular region.

Finally, we multiply by the cost factor of $1.25 per square foot:

Cost = (3600 sq. ft.)($1.25 per sq. ft.) = $4500

The correct choice is C.