Basic College Mathematics (9th Edition)

Published by Pearson
ISBN 10: 0321825535
ISBN 13: 978-0-32182-553-7

Chapter 8 - Geometry - 8.4 Parallelograms and Trapezoids - 8.4 Exercises: 22

Answer

Total area of the shape = 5905.9 cm$^{2}$

Work Step by Step

To find the are of the shape we simply need to break the shape into two separate trapezoids, find the area of each trapezoid, and add the results together. Area of a Trapezoid = $A$ = $\frac{1}{2}$$h$($b$ + $B$) Therefore: $A$$_{top}$ = $\frac{1}{2}$(46.2 cm)(61.7 cm + 87.3 cm) $A$$_{top}$ = $\frac{1}{2}$(46.2 cm)(149 cm) $A$$_{top}$ = (23.1 cm)(149 cm) $A$$_{top}$ = 3441.9 cm$^{2}$ $A$$_{bottom}$ = $\frac{1}{2}$(46.2 cm)(61.7 cm + 92.3 cm) $A$$_{bottom}$ = $\frac{1}{2}$(32 cm)(154 cm) $A$$_{bottom}$ = (16 cm)(154 cm) $A$$_{bottom}$ = 2464 cm$^{2}$ Total Area = $A$$_{total}$ = $A$$_{top}$ + $A$$_{bottom}$ $A$$_{total}$ = 3441.9 cm$^{2}$ + 2464 cm$^{2}$ $A$$_{total}$ = 5905.9 cm$^{2}$
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