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Math in the Workplace: Overview

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Math in the Work Place

Math in the Workplace - Measurements/Geometry

JAMES GIPSON ASSOCIATES

Architecture & Planning
Architect

 


Problem:

#1 John and Joan are planning a new home. They want as much window area as possible. The local energy code permits a maximum window area of 17% of the house floor area.

The windows John and Joan will use are each 3 ft. x 5 ft. and the floor area of the house is 1,720 square feet. How many windows can they put into their new house?

#2 diagramKaren is figuring how many bundles of shingles to order for the roof on a garage. The garage is 24 ft. x 24 ft., with a single roof ridge down the middle, plus a 2 ft. overhang all around.

Three bundles of shingles are required for each 100 sq. ft. of roof. How many bundles of shingles should Karen order?

solution

return to top JAMES GIPSON ASSOCIATES


Solution:

#1 17% of 1,720 sq. ft. = 292.4 sq. ft.

Each window is 3' x 5' or 15 sq. ft.

292.4 15 = 19.49
Therefore, John and Joan can have at most 19 windows.

 

#2 Consider the end view of the roof as two right triangles, each with a base of 12' + 2' = 14' and a height of 7'.
diagram

    a2 + b2 = c2
    72 + 142 = c2 = 245 sq. ft.
    c= 15.65 sq. ft.
    Area of half the roof = 15.65' x (24'+ 4') = 438.2 sq. ft.
    Area of the roof = 438.2 x 2 = 876.4 sq. ft.

The number of shingle bundles required = area of roof 33 1/3

    876.4 33 1/3 = 26.29

Therefore, Karen should order 27 bundles.