Find the area of the shaded region in figure, where arcs drawn with centers A, B, C and D intersect in pairs at mid-point P, Q, R and S of the sides AB, BC, CD and DA, respectively of a square ABCD. (use π = 3.14)

Question

Philoid · Accepted Answer

Since P, Q, R and S divides AB, BC, CD and DA in half.

∴ AP = PB = BQ = QC = CR = RD = DS = SA = 6 cm.

Given, side of a square BC = 12 cm

Area of the square = 12 × 12 = 144 cm²

Area of the shaded region = Area of the square - (Area of the four quadrants)

Area of one quadrant = (π/4)×(Radius)² = (3.14/4)× 36 = 113.04/4 cm²

Area of four quadrants = 113.04 cm²

Area of the shaded region = 144-113.04 = 30.96 cm²