Elementary and Intermediate Algebra: Concepts & Applications (6th Edition)

Published by Pearson
ISBN 10: 0-32184-874-8
ISBN 13: 978-0-32184-874-1

Chapter 4 - Polynomials - Review Exercises: Chapter 4: 69

Answer

The area of the shaded region is $\frac{1}{2}(x^2-y^2)$ square units.

Work Step by Step

RECALL: (1) The area $A$ of a triangle is given by the formula $A=\frac{1}{2}bh$ where $b$=base and $h$=height. (2) $(a-b)(a+b)=a^2-b^2$ The given triangle has a base of $x+y$ and a height of $x-y$. Use the formula in (1) above to obtain: $A=\frac{1}{2}(x+y)(x-y)$ Use the formula in (2) above to obtain: $A=\frac{1}{2}(x^2-y^2)$ Thus, the area of the shaded region is $A=\frac{1}{2}(x^2-y^2)$ square units.
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