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In the given figure $ABCDE$ is a pentagonal park in which $DE = DC, AB = BC = CE = EA = 25 m$ and its total height is $41 m$ . What is the area of the park?

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{225 cm}^{2}

{525 cm}^{2}

{625 cm}^{2}

{825 cm}^{2}

answer is D.

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Detailed Solution

Given that the figure

ABCDE

where

DE = DC, AB = BC = CE = EA = 25 m

and its total height is

41 m

Area of a square is

sid e^{2}

.
Area of a triangle is

\frac{1}{2} (base) (height)

.
Height of triangle

= 41 - 25 = 16 cm

.
Area of park

=

area of square

ABCE +

area of

ΔDEC

\Rightarrow

Area of park

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

\Rightarrow

Area of park

= 25 \times 25 + \frac{1}{2} \times 25 \times 16

\Rightarrow

Area of park

= 625 + 200

\Rightarrow

Area of park

= {825 cm}^{2}

Hence, option 4 is correct.

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In the given figure ABCDE is a pentagonal park in whichDE=DC,AB=BC=CE=EA=25m and its total height is 41m. What is the area of the park?

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In the given figure $ABCDE$ is a pentagonal park in which $DE = DC, AB = BC = CE = EA = 25 m$ and its total height is $41 m$ . What is the area of the park?