(Q15) Calculate the area of the designed region in figure, common between the two quadrants of the circles of radius 10 cm each (use π)

Mark two points P,Q on the either acrs

Let BD be a diagonal of ABCD

Now the area of the segment

DPB = Area of sector ADPB - Area of triangle ABD

=
x
360
 πr2 -
1
2
 bh
=
360
 ×
22
7
 ×× -
1
2
 ××

= .57 -

= .5 cm2

Similarly , area of the segment DQB = .5 cm2

Area of the shaded region

=(DPB+DQB) segments

= .5+.5 = cm2

Side of the square = 10 cm

Area of the square = side×side

= × = cm2

Area of two sectors with centers A and C amd radius 10 cm

= 2 ×
πr2
360
 ×x = 2×
x
360
 ×
22
7
 ××
=
7

= .14cm2

Designed area is common to both the sectors

Area of design = Area of both sectors - Area of square

= - = cm2