Given the dimensions of the following polygon, find the area of each of the following.
(a) Triangle of base $(2 x - 2 y)$ units and height $(x + y)$ units
(b) Rectangle of side $(4 a + 5 b)$ units and $(4 a - 5 b)$ units
(c) Square of side $(5 a + b)$ units

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Solution

(a)area of triangle= $\frac{1}{2} (2 x - 2 y) (x + y) = x^{2} - y^{2}$

(b)area of rectangle = $(4 a + 5 b) (4 a - 5 b) = 16 a^{2} - 25 b^{2}$

(c)area of square = $(s i d e)^{2} = (5 a + b)^{2}$
$= 25 a^{2} + b^{2} + 10 a b$

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