EXAMPLE 2.6.5

The diagram below shows one exterior wall of a house. The wall has a door opening that measures 3 feet by 7 feet, and two window openings that each measure 6 feet by 4 feet. The wall, but not the openings, will be covered with siding material that costs $1.50 per square foot. Find the total cost of the siding material.

A. $400.50

B. $292.50

C. $499.50

D. $333.00

SOLUTION

To solve this problem we need to compute the area (in square feet) of the region to be covered with siding material, and then multiply by the cost factor of $1.50 per square foot.

The region to be covered consists of a rectangular region, plus a triangular region, minus the combined areas of the two rectangular windows and the rectangular door.

Recall that for a rectangle

Area = LW

Area of large rectangle = (24 feet)(8 feet) = 192 sq. ft.

Area of each window = (6 feet)(4 feet) = 24 sq. ft.

Area of door = (3 feet)(7 feet) = 21 sq. ft.

Recall that for a triangle

Area = (1/2)bh

Area = (1/2)(24 feet)(6 feet) = 72 sq. ft.

The total area to be covered is the area of the large rectangle plus the area of the triangle minus the areas of the two windows and the door:

192 + 72 - 24 - 24 - 21 = 195 sq. ft.

Finally,

Cost = (195 sq. ft.)($1.50 per sq. ft.) = $292.50