Find the area of the shaded region in figure, where arcs drawn with ce

1.	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)
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

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)

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