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Calculate the area of the shaded region of the following 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}

455 c m^{2}

450 c m^{2}

350 c m^{2}

answer is C.

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Detailed Solution

Given,
Length l=30 cm
breadth b=20 cm
Area of rectangle

= l \times b

= 30 \times 20

= 600 c m^{2}

Now, in

ΔDGF,

Length, DF=15 cm
Breadth, DG=10 cm

So, area of ΔDGF

= \frac{1}{2} \times b \times h

= \frac{1}{2} \times 15 \times 10

= 75 c m^{2}

Similarly, triangle AGE’s area is

75 c m^{2}

Thus, shaded region area,

= 600 - (75 + 75) = 600 - 150 = 450 c m^{2}

Hence, the correct answer is 3.

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