In Fig, ABC is a quadrant of a circle of radius 14 cm and a semicircle is drawn with BC as diameter. Find the area of the shaded region.
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Solution
Radius of the the quadrant ABC of circle = 14 cm
AB = AC = 14 cm
BC is diameter of thesemicircle.
ABC is a right angled triangle.
By Pythagoras theorem in ΔABC, BC2=AB2+AC2 ⇒BC2=142+142 ⇒BC=14√2cm
Radius of semicircle =14√22cm=7√2cm
Area of ΔABC=12×14×14=98cm2
Area of quadrant =14×227×14×14=154cm2
Area of the semicircle =12×227×7√2×7√2=154cm2
Area of the shaded region = Area of the semicircle + Area of ΔABC - Area of quadrant =154+98−154cm2=98cm2