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$ABCD$ is a rectangle having length $30 cm$ and breadth $25 cm, P, Q, R, and S$ are midpoints of $AB, BC, CD$ and $AD$ respectively. What is the area of the shaded region of the figure?

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375 c m^{2}

370 c m^{2}

475 c m^{2}

450 c m^{2}

answer is A.

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Detailed Solution

Given,

ABCD

is a rectangle having length

30 cm

and breadth

25 cm, P, Q, R, and S

are midpoints of

AB, BC, CD

and

AD

respectively.
Question Image

Area of a rectangle is (length)×(breadth).
Area of

△ SDR

= Area of

△ RCQ

= Area of

△ PBQ

= Area of

△ PAS

Area of rectangle =

30 \times 25 = 750 c m^{2}

.
Area of each unshaded triangle is

\frac{1}{8} (Area of the rectangle)

since, P, Q, R, S are midpoints.
Area of triangle

△ SDR

= \frac{1}{8} (area of the rectangle)

\Rightarrow

Area of triangle

△ SDR

= \frac{1}{8} (750)

\Rightarrow

Area of triangle

△ SDR

= 93.75 c m^{2}

Area of shaded region

=

Area of rectangle

-

Area of all

4

triangles.
Area of shaded region

= 750 - 4 \times 93.75

\Rightarrow

Area of shaded region

= {375 cm}^{2}

Hence, option 1 is correct.

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ABCD is a rectangle having length 30 cm and breadth 25 cm, P, Q, R,and S are midpoints of AB,BC,CD and AD respectively. What is the area of the shaded region of the figure?

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$ABCD$ is a rectangle having length $30 cm$ and breadth $25 cm, P, Q, R, and S$ are midpoints of $AB, BC, CD$ and $AD$ respectively. What is the area of the shaded region of the figure?