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Q.

Find the area of a square inscribed in a circle whose radius is 7 cm.


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a

98c m 2

b

49c m 2

c

112c m 2

d

None of these 

answer is A.

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Detailed Solution

Given, a circle whose radius is 7 cm.
Question ImageWe know that the area of a triangle is half the product of its base length and its height.
Now, as per the figure given, we can observe that the two diameters of the circle divide it into four right angled triangles as the diagonals of a square intersect each other at right angles.
So, the area of the square will be the area of the four triangles.
So, we have,
Area of triangle= 1 2 ×base×height
Now, as can be observed, the base and the height of each of the four triangles is nothing but the radius of the circle, which is given as 7 cm.
So, the area of the square is as follows,
= 1 2 ×7×7 = 1 2 ×49 =24.5 cm 2
Area of square=4×Area of triangle =4×24 .5cm 2 =98c m 2
So, the area of the inscribed square is found as 98c m 2 .
Hence, the correct option is (1).
 
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