Question

6. If the side of a square is 14 cm. find the area of circumscribed circle. a) 68 πcm2? b) 78π cm2 c) 88π cm2? d) 98π
cm2?​

Answer 1

SOLUTION

TO CHOOSE THE CORRECT OPTION

The side of a square is 14 cm. The area of circumscribed circle

a) 68π cm²

b) 78π cm²

c) 88π cm²

d) 98π cm²

EVALUATION

Here it is given that the side of a square is 14 cm

Length of the diagonal of the square

$\sf = Side \times \sqrt{2}$

$\sf = 14 \times \sqrt{2} \: \: cm$

$\sf = 14 \sqrt{2} \: \: cm$

Since the circle is circumscribed the square

Diameter of the circle = Length of the diagonal of the square

So radius of the circle

$\displaystyle \sf{ = \frac{14 \sqrt{2} }{2} } \: \: cm$

$\displaystyle \sf{ = 7 \sqrt{2} } \: \: cm$

Hence the required area of circumscribed circle

$\displaystyle \sf{ = \pi {r}^{2} \: \: {cm}^{2} }$

$\displaystyle \sf{ = \pi \times {(7 \sqrt{2}) }^{2} \: \: {cm}^{2} }$

$\displaystyle \sf{ = \pi \times 7 \times 7 \times 2 \: \: {cm}^{2} }$

$\displaystyle \sf{ = 98\pi \: \: {cm}^{2} }$

FINAL ANSWER

Hence the correct option is d) 98π cm²

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