Find the area of the pentagonal park shown in figure in two different ways.

600 m^{2}

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800 m^{2}

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60 m^{2}

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600 c m^{2}

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Solution

The correct option is A $600 m^{2}$

In first case :- Area of park = at trap. $A E D M$ + ar. trap $B M D C$
$=$ $\frac{1}{2} (A E + D M) \times E N + \frac{1}{2} (A E + D M) \times C N$
$=$ $\frac{1}{2} (A E + D M) (E N + C N) = \frac{1}{2} (A E + D M) E C$

$=$ $\frac{1}{2} (20 + 40) \times 20 = 600 m^{2}$
In second case : Area of park $=$ $a r Δ E D C + a r A B C P$
$=$ $\frac{1}{2} \times E C \times D M + A B \times C E$
$=$ $\frac{1}{2} \times 20 \times (40 - 20) + 20 \times 20$
$=$ $200 + 400 = 600$ $m^{2}$

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There is a pentagonal shaped park as shown in the figure. Jyoti and Kavita divided it in two different ways.

Find the area of this park using both ways. Can you suggest another way of finding its area?

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