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In the following figure, arcs have been drawn of radius $21$ cm each with vertices A, B, C and D of quadrilateral ABCD as centres. The area of the shaded region from the choices given below is:

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693 cm 2

231 cm 2

1098 cm 2

1386 cm 2

answer is D.

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Detailed Solution

It is given that, radius is

21

cm.

Obtain the area of all the four sector.
Here, the area of each sector is equal.
And we know that, the sum of all interior angle in any quadrilateral is

360 °

.
Central angle of each sector is obtained by,

= \frac{360 °}{4}

= 90°
Thus, the central angle of each sector is

90 °

.
So, the area of each sector is,

A = \frac{πr^{2} θ}{360 °}

= \frac{π (21)^{2} 90 °}{360 °}

= 10.25 π cm^{2}

Obtain the area of the shaded region.
We get,

A s = 4 A A s = 4 × 10.25 π A s = 1386 cm 2

The area of the shaded region is

1386 cm 2

.
Hence, option 4) is correct.

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