Question

In the adjoining figure abcd is a square of side 14 cm. A,B,c.d are centres of circular arcs of equal radius. Find the perimeter and the area of shaded region
answer is 44cm and 42 cm. Sq. I know the answer but how

Answer 1

As you've already found out from diagram, since the circles are of equal radius and it divides the side of the "square" thus the radius of the circle is 14/2 = 7 cm


Now, the angle made by each part of the circle is 90 thus the four parts are quadrants of the circle and the four parts make one circle of radius 7 cm.

For perimeter, we have to find perimeter of the circle which is 2*pi*r = 2*22/7*7= 44 cm
and area = area of square - area of circle
               = 4*side of square - pie*r2