In the given figure ABCDE is a pentagon in which $D E = D C, A B = B C = C E = E A = 25 m$ and its total height is $41 m$ . Find the area of the pentagon.

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Solution

Area of pentagon is=Area of square ABCE+Area of triangle EDC
Area of triangle is $\frac{1}{2}$ base $\times$ height.
Height $= 41 - 25 = 16$
Base $= 25$
$∴ \frac{1}{2} \times 25 \times 16 = 200 m^{2}$
Area of square $= a^{2}$
$= 25^{2} = 625 m^{2}$
Area of pentagon is $625 m^{2} + 200 m^{2}$
$= 825 m^{2}$

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