Elementary Geometry for College Students (6th Edition)

Published by Brooks Cole
ISBN 10: 9781285195698
ISBN 13: 978-1-28519-569-8

Chapter 8 - Section 8.2 - Perimeter and Area of Polygons - Exercises - Page 360: 26


a$\sqrt s^{2} - a^{2}$

Work Step by Step

Using Heron's formula if three sides of a triangle have length a,b,c then area A of a triangle is A = $\sqrt s(s-a)(s-b)(s-c)$ where s = $\frac{a+b+c}{2}$ Lets take a=QM = s, b=QN = s and c=MN = 2a s = $\frac{s+s+2a}{2}$ = $\frac{2s+2a}{2}$ =s+a A = $\sqrt (s+a)(s+a-s)(s+a-s)(s+a-2a)$ =$\sqrt (s+a)*a*a*(s-a)$ =a$\sqrt s^{2} - a^{2}$ (Since (a+b)(a-b) = $a^{2}$ - $b^{2}$)
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