Precalculus (10th Edition)

Published by Pearson
ISBN 10: 0-32197-907-9
ISBN 13: 978-0-32197-907-0

Chapter 8 - Applications of Trigonometric Functions - 8.4 Area of a Triangle - 8.4 Assess Your Understanding - Page 544: 37



Work Step by Step

By Heron's formula, $K=\sqrt{s(s-a)(s-b)(s-c)}$, where $s=\frac{a+b+c}{2}.$ Hence, here $s=\frac{100+50+75}{2}=112.5$ Thus, $K=\sqrt{112.5(112.5-100)(112.5-50)(112.5-75)}\approx1815.46.$ The unit price is $3$ dollars per square foot. Multiply the area and the cost per square foot to obtain: Total cost = $\$3(1815.46)=\$5,446.38$
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