# Four Equal Circles Are Described About the Four Corners of a Square So that Each Touches Two of the Others, as Shown in the Figure. Find the Area of the Shaded Region, If Each Side of the - Mathematics

Sum

Four equal circles are described about the four corners of a square so that each touches two of the others, as shown in the figure. Find the area of the shaded region, if each side of the square measures 14 cm.

#### Solution

Side of the square = 14 cm
Radius of the circle =14/2 = 7 "cm"
Area of the quadrant of one circle = 1/4pi"r"^2

=1/4xx22/7xx7xx7

= 38.5 cm

Area of the quadrants of four circles = 38.5 × 4 = 154 cm

Now,
Area of the square =(Side)

= 14

= 196 cm

Area of the shaded region = Area of the square -- Area of the quadrants of four circles

= 196 - 154

= 42 cm

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#### APPEARS IN

RS Aggarwal Secondary School Class 10 Maths
Chapter 18 Area of Circle, Sector and Segment
Exercise 18B | Q 36 | Page 833