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Calculate the area of the shaded region of the given figure. $ABCD$ is a rectangle having length $30 cm$ , breadth $20 cm$ . $E, F$ and $G$ are midpoints of $AB, CD$ and $AD$ respectively.

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400 c m^{2}

450 c m^{2}

375 c m^{2}

325 c m^{2}

answer is B.

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Detailed Solution

It is given that,
ABCD is a rectangle having length 30 cm and breadth 20 cm.

∴ AB = CD = 30 cm and AD = BC = 20 cm

Since, E, F, and G are mid-points of

AB, CD

and

AD

respectively therefore,

AE = \frac{1}{2} AB = 15 cm

AG = GD = \frac{1}{2} AD = 10 cm

And

DF = \frac{1}{2} DC = 15 cm

Now,
Area of rectangle

= length \times breadth

∴ ar (ABCD) = 30 \times 20

= 600 {cm}^{2}

Area of triangle

= \frac{1}{2} \times Base \times Height

∴ ar (△ GDF) = \frac{1}{2} \times GD \times DF

\Rightarrow ar (△ GDF) = \frac{1}{2} \times 10 \times 15

= 75 c m^{2}

And

ar (△ GAE) = \frac{1}{2} \times GA \times AE

\Rightarrow ar (△ GAE) = \frac{1}{2} \times 10 \times 15

= 75 c m^{2}

From figure,

Area of shaded region = Area of rectangle - Area of both triangles

\Rightarrow Area of shaded region

= 600 - 75 - 75

= 450 c m^{2}

Therefore,

Area of shaded region = 450 c m^{2}

Hence, option (2) is correct.

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