A circle has a radius of 12 units and its center is at one vertex of a square. Find the area of the shaded region?

Question

A circle has a radius of 12 units and its center is at one vertex of a square. The square has a side of 12 units. Find the area of the shaded region?

Answer 1

Area of shaded region = Half the area of square.
i.e., (12*12)/2 = 72 sq. units

Answer 2

area of yellow sector inside circle=144*pi/8=56.54862 sq cm
therefore area of both sectors= 113.09724 sq cm
area outside the circle= 144-113.09724 = 30.90276 sq cm
thus yellow area outside circle = 15.45138 sq cm
hence whole yellow area= 56.54862+15.45138=72 sq cm

without calculations
since white area and yellow area are same each=0.5*144=72 sq cm

Answer 3

This can be solved visually by looking at the shaded bisected area of the upper left hand corner and concluding that
it forms 1/2 of the square.

thus: 1/2*144 = 72

Answer 4

The area of the shaded region = half of the square =12x12/2= 72 unit^2