Elementary Geometry for College Students (5th Edition)

Published by Brooks Cole
ISBN 10: 1439047901
ISBN 13: 978-1-43904-790-3

Chapter 8 - Section 8.1 - Area and Initial Postulates - Exercises - Page 360: 26a

Answer

Total area to be shingled = 1560 ft

Work Step by Step

We want to shingle the total area of the roof. Because of the roof's symmetry, we can find the area of one slant and multiply by two. The length of the roof is 60 ft, and we need to use the Pythagorean theorem to find the width of the roof's component, as it serves as the hypotenuse for the attic. Dividing the side length of the house by 2, we have $w=\sqrt{5^2+12^2}=\sqrt{25+144}=13$. The area of the roof, now including both components, is $a=(2)(60)(13)=1560$ ft.
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