Find the area of the shaded region in Figure, where arcs drawn with centres A, B, C and D intersect in pairs at mid-points P, Q, R and S of the sides AB, BC, CD and DA, respectively of a square ABCD (Use = 3.14).
[30.96 cm2]
Solution
Here ABCD is a square of side 12 cm
Area of ABCD= (side)2=(12)2=144 cm2
Area of sector = here
Here PSAP, PQBP, QRCQ, RSDR all sectors are equal
Area of 4 sectors =
Area of shaded region = Area of square – Area of 4 sectors
= 144-113.04
=30.96 cm2