Question

13. find the area of shaded region shown in the given figure where a circular arc of radius 6 cm has
been drawn with vertex 'O' of an equilateral A OAB of side 12 cm as centre.​

Answer 1

Step-by-step explanation:

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Find the area of the shaded region in Fig. 12.22, where a circular arc of radius 6 cm has been drawn with vertex O of an equilateral triangle OAB of side 12 cm as centre.

It is given that side of equilateral triangle = 12 cm.

fraction numerator square root of 3 over denominator 4 end fraction space space side squared

Therefore,    area = 

open parentheses fraction numerator square root of 3 straight x space 12 space straight x space 12 over denominator 4 end fraction close parentheses space cm squared equals space 36 square root of 3 space cm squared

                           =  

Let radius of the circle be r, then

r = 6 cm.

Therefore,  area = 

πr squared

22 over 7 space straight x space 6 space straight x space 6 space equals space 792 over 7 space space cm squared

                         = 

Now, 

Area of a sector of a circle of radius 6 cm and of angle 60

.

degree