Q28 of 180 Page 2

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)


OR


Find the area of the flower bed (with semi – circular ends) shown in figure. (Use π = 3.14)



Since P, Q, R and S are the mid points of AB, BC, CD and DA.


∴ 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 four quadrants = 4 × × r2 = π r2 = 3.14 × (6)2 = 113.04 cm2


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


OR


Length and breadth of the rectangular portion AFDC of the flower bed are 38 cm and 10 cm respectively.


Area of the flower bed = Area of the rectangular portion + Area of the two semi – circles.



∴ Area of rectangle AFDC = Length × Breadth


= 38 × 10 = 380 cm2


Both ends of flower bed are semi – circle in shape.


∴ Diameter of the semi – circle = Breadth of the rectangle AFDC = 10 cm


∴ Radius of the semi-circle = 10/2 = 5 cm


Area of the semi – circle = πr2/2 = 25π/2 cm2


Since there are two semi – circles in the flower bed,


∴ Area of two semi – circles = 2 × 25π/2 = 25 ×3.14 = 78.5 cm2


Total area of flower bed = 380 + 78.5 = 458.5 cm2


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