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: 27

Answer

The area of the given figure, according to the variables shown is\[A=2{{a}^{2}}+ab\].

Work Step by Step

We have to find a formula for the area of the given figure. The figure consist of two squares, each of side a units and a rhombus of sides equal to a units and height equal to b units. For finding out the formula, we have to add the formulas of the figures that make up this figure, according to the given variables. Area of a square of side a units as a follows: \[{{A}_{1}}={{a}^{2}}\] Area of a rhombus of sides equal to a units and height equal to b units is as follows: \[{{A}_{2}}=ab\] So, the total area of the figure will be as follows: \[\begin{align} & A={{a}^{2}}+{{a}^{2}}+ab \\ & =2{{a}^{2}}+ab\text{ } \end{align}\] Hence, the area of the given figure, according to the variables shown is\[A=2{{a}^{2}}+ab\].
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