Sir please help me to solve the ncert class 10 areas related to circles of exercise 12.3 question no. 7 . Find the easiest and simplest way to solve this question also find the best and easiest way to solve this question.In Fig. 12.25, ABCD is a square of side 14 cm. With centres A, B, C and D, four circles are drawn such that each circle touch externally two of the remaining three circles. Find the area of the shaded region.
Side of square = 14 cm
Four quadrants are included in the four sides of the square.
∴ Radius of the circles = 14/2 cm = 7 cm
Area of the square ABCD = 142 = 196 cm2
Area of the quadrant = (πR2)/4 cm2 = (22/7) ×72/4 cm2
= 77/2 cm2
Total area of the quadrant = 4×77/2 cm2 = 154cm2
Area of the shaded region = Area of the square ABCD – Area of the quadrant
= 196 cm2 – 154 cm2
= 42 cm2