Find the area of the shaded region where ABC is a quadrant of radius 5 cm and a semicircle is drawn with BC as diameter.
12.5 cm2
Area of the shaded region = Area of semicircle-Area of segment BXC
Here, AB = AC = 5 cm
Then, by Pythagoras theorem,
BC2=AB2+AC2BC2=52+52BC2=50BC=5√2 cm
Area of the semicircle with BC as diameter
=12×227×5√22×5√22=12×227×5√2×5√2
=19.64 cm2...(i)
Area of segment BXC = Area of quadrant - Area of ΔABC
=90°360°×227×52−12×5×5
=19.64−12.5
=7.14 cm2...(ii)
Area of the shaded region = Area of semicircle with BC as diameter - Area of Segment BXC
=19.64−7.14
=12.5 cm2