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 - Page 627: 29



Work Step by Step

$$a^{2}+b^{2}=c^{2}$$ $1^{2}+b^{2}=3^{2}$ $1+b^{2}=9$ $b^{2}=8$ $b=2\sqrt 2$ $b=2.828$ To find the height of the trapezoid, use the Pythagorean theorem with the two lengths of the triangle provided: $$A=\frac{1}{2}(b_{1}+b_{2})h$$ $A=\frac{1}{2}(5+3)2.828$ $A=11.312$ $A=11.3 cm^{2}$ To find the area of the trapezoid, use the trapezoid area formula and plug in the height of the triangle we found previously. Following that, solve for A.
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