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Find the area of the shaded region in the given figure.

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244 m^{2}

(248 - 4 π) m^{2}

242 m^{2}

248 m^{2}

answer is A.

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Detailed Solution

Given a rectangle of length 26 m and breadth 12 m.
Question Image

We know that, the area of semi-circle is

π r 2 2

.
Finding the diameter of each semicircle.

12 − 4 + 4 = 4

The diameter of each semicircle is 4 m. So, its radius 2 cm.
Calculating the area of two semi-circles,

2 12 π r 2 = π 22

= 4 π m 2

Calculating the length of inner rectangle, and then area of inner rectangle.

f × b = 16 × 4

⇒

m 2

Calculating the area of outer rectangle.

L × B = 26 × 12

⇒ 312 m 2

Finding the area of shaded region subtract the sum of the area of two semi circles and the area of inner rectangle from the area of the outer rectangle.

312 − 64 + 4 π = 248 − 4 π m 2

Therefore, area of the shaded region is

248 − 4 π m 2

.
Hence the correct option is 1.

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