Elementary Geometry for College Students (7th Edition) Clone

Published by Cengage
ISBN 10: 978-1-337-61408-5
ISBN 13: 978-1-33761-408-5

Chapter 8 - Section 8.2 - Perimeter and Area of Polygons - Exercises - Page 370: 12

Answer

30$cm^{2}$

Work Step by Step

Given, AB = 6 cm, BC =7cm CD =2 cm, DA = 9 cm By Brahmaguptas formula, the area of cyclic quadrilateral with sides of length a,b,c and d is A = $\sqrt (s-a)(s-b)(s-c)(s-d)$ s = $\frac{a+b+c +d}{2}$ AB =a = 6 cm, BC = b = 7 cm CD = c =2 cm, DA = d = 9 cm s = $\frac{6+7+2+9}{2}$ =12 cm A = $\sqrt (12-6)(12 - 7)(12 - 2)(12 - 9)$ =$\sqrt 6*5*10*3$ =30$cm^{2}$ Therefore the area of the cyclic quadrilateral ABCD = 30$cm^{2}$.
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