Question

four equal circles are described about the four corners of a square so that each circle touches two of the others .find the area of the space enclosed between the circumference of the circles,each side of the square measuring 14 centimetre.

Answer 1

let ABCD be the sides of the square
side of square =14cm
Area of the Square A =14x14
A=196sq.cm
The radius 'r'of each circle =14/2
r=7cm

area of the four quadrant at the four corners of the square =pir^2
=(22x7x7))7
=154sq.cm
therefore area of the space enclosed by the circumference of the circle =Area of square -4x(1/4 of area of each circle) [since there are 4 quadrant ]
=196-area of one circle
=196-154sq.cm
=42sq.cm