Geometry: Common Core (15th Edition)

Published by Prentice Hall
ISBN 10: 0133281159
ISBN 13: 978-0-13328-115-6

Chapter 10 - Area - 10-1 Areas of Parallelograms and Triangles - Practice and Problem-Solving Exercises: 45

Answer

126 m$^{2}$

Work Step by Step

A = $\sqrt {s(s−a)(s−b)(s−c)}$, where s = $\frac{1}{2}$(a+b+c) a = 15 b = 17 c = 21 To simplify the equation and to make the computation process easier, solve for "s" first. s = $\frac{1}{2}$(a+b+c) = $\frac{1}{2}$(15+17+21) = $\frac{1}{2}$(53) = 26.5 Now, substitute 26.5 into the original equation every time "s" appears. A = $\sqrt {s(s−a)(s−b)(s−c)}$ A = $\sqrt {26.5(26.5−a)(26.5−b)(26.5−c)}$ A = $\sqrt {26.5(26.5−15)(26.5−17)(26.5−21)}$ A = $\sqrt {26.5(11.5)(9.5)(5.5)}$ A = $\sqrt {15,923.1875}$ A ≈ 126. 2 126.2 rounded to the nearest whole number is 126.
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