Geometry: Common Core (15th Edition)

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

Chapter 10 - Area - 10-2 Areas of Trapezoids, Rhombuses, and Kites - Practice and Problem-Solving Exercises: 25

Answer

24 $m^{2}$

Work Step by Step

Find the length of the other diagonal by using the Pythagorean Theorem. Create a triangle cutting the diagonal given in half. This gives you a base to your triangle of 3. $a^{2}$+$b^{2}$=$c^{2}$ $3^{2}$+$b^{2}$=$5^{2}$ 9 + $b^{2}$=25 $b^{2}$=16 b=4 The diagonal is twice this length. 4x2=8 We use the formula for the area of a rhombus to obtain: A=$\frac{1}{2}$($d_{1}$)($d_{2}$) A=$\frac{1}{2}$(8)(6) A=24
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