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A pentagon is divided in two different ways by Aditya and Noni as shown in the figure. Find the area of this pentagon using both ways.

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450 c m^{2}

410 c m^{2}

480 c m^{2}

486 c m^{2}

answer is D.

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Detailed Solution

Aditya' s diagram

Area of pentagon = Area of triangle + Area of Square

= \frac{1}{2} \times base \times height + sid e^{2}

= \frac{1}{2} \times 18 \times (36 - 18) + 18^{2}

= 486 c m^{2}

Noni' s diagram

Area of pentagon = 2 \times Area of trapezium

= 2 \times \frac{1}{2} \times (Sum of parallel sides) \times height

= (18 + 36) \times 9

= 486 c m^{2}

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