Thinking Mathematically (6th Edition)

Published by Pearson
ISBN 10: 0321867327
ISBN 13: 978-0-32186-732-2

Chapter 10 - Geometry - 10.4 Area and Circumference - Exercise Set 10.4 - Page 647: 22

Answer

The area of the figure is: \[\text{70}\text{.5 c}{{\text{m}}^{2}}\]

Work Step by Step

Area of given figure will be calculated by finding the area of the rectangle and area of trapezium given in the figure and then adding the area of that trapezium and rectangle. The area is expressed as the space enclosed between closed figures to the extent of a two-dimensional figure. Use the formula to determine the area of the figure as shown below, \[\begin{align} & \text{Area of rectangle}=l\times b \\ & =\text{6 cm}\times 3\text{ cm} \\ & =18\text{ c}{{\text{m}}^{2}} \end{align}\] Compute the area of the trapezium as follows, $\begin{align} & \text{Area of trapezium = }\frac{1}{2}\times \left( a+b \right)h \\ & \text{= }\frac{1}{2}\times \left( 9+6 \right)\times 7 \\ & =52.5\text{ c}{{\text{m}}^{2}} \end{align}$ Compute the area of the given figure by adding the area of the rectangle and area of the trapezium as shown below, $\begin{align} & \text{Area of given figure}=\text{Area of rectangle}+\text{Area of triangle} \\ & =\text{18 c}{{\text{m}}^{2}}+\text{52}\text{.5 c}{{\text{m}}^{2}} \\ & =70.5\text{ c}{{\text{m}}^{2}} \end{align}$ Hence, the area of the provided figure is, \[\text{70}\text{.5 c}{{\text{m}}^{2}}\].
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