Math in the Workplace: Overview

Math in the Workplace - Geometry Problems

Problem:

A customer would like a bonus room to be added to be added to an existing home. The new room is to be 26' x 24' with an 8' celling and a 2' roof overhang. The ridge of the roof is to be centered over the 24 foot wall and 5 feet above the top of the wall of the bonus room.

Assuming the builder uses standard 4' x 8' plywood sheets, determine the following:

1. How many plywood sheets will be needed to cover the walls of the bonus room (not accounting for doors or windows).

2. How many plywood sheets will be necessary to cover the roof over the bonus room.

DAN ROMAN CONSTRUCTION

Solution:

1. To find how many sheets will be necessary for the 4 walls, divide the area of the walls by the area of a plywood sheet (not allowing for doors or windows).

(2 walls) (26' x 8') + (2 walls) (24' x 8') 4' x 8' plywood sheet

(2 x 208 sq ft) + (2 x 192 sq ft) 32 sq ft

=

416 sq ft + 384 sq ft 32 sq ft

800 sq ft 32 sq ft

= 25 sheets of plywood for the walls.

2. To find how many sheets will be necessary for the roof, divide the total area of the roof (2 equal sides) by the area of a plywood sheet.

The ridge of the roof is 26 feet and the overhang is 2 feet. The height of the roof is 5 feet. Find the area of each side of the roof by calculating the length from the ridge to the edge (a² + b² = c²), adding the overhang, and multiplying the total length by the width (ridge).

5² + 12² = c²

25 x 144 = C²

C= 13 ft

Roof area: (2' + 13') x 26' = 390 sq ft x 2 (both sides) = 780 sq ft

Now divide by the plywood sheet dimension:

780 sq ft 4'x8' sheets

= 24.375 or 25 sheets of plywood for the roof

Math in the Workplace: Overview