Today i am solving the ncert class 10 areas related to circles of exercise 12.3 question no. 3 . How i solve the best solution of this question please help me to find out the easiest solution of this question.Find the area of the shaded region in Fig. 12.21, if ABCD is a square of side 14 cm and APD and BPC are semicircles.
Side of the square ABCD (as given) = 14 cm
So, Area of ABCD = a2
= 14×14 cm2 = 196 cm2
We know that the side of the square = diameter of the circle = 14 cm
So, side of the square = diameter of the semicircle = 14 cm
∴ Radius of the semicircle = 7 cm
Now, area of the semicircle = (πR2)/2
= (22/7×7×7)/2 cm2 =
= 77 cm2
∴ Area of two semicircles = 2×77 cm2 = 154 cm2
Hence, area of the shaded region = Area of the Square – Area of two semicircles
= 196 cm2 -154 cm2
= 42 cm2