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26/06/2021 1:27 pm
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In Figure, 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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26/06/2021 1:29 pm
Radius of the quadrant ABC of circle = 14 cm
AB = AC = 14 cm
BC is diameter of semicircle.
ABC is right angled triangle.
By Pythagoras theorem in ΔABC,
BC2 = AB2 +AC2
⇒ BC2 = 142 +142
⇒ BC = 14√2 cm
Radius of semicircle = 14√2/2 cm = 7√2 cm
Area of ΔABC =( 1/2) × 14 × 14 = 98 cm2
Area of quadrant = (1/4) × (22/7) × (14 × 14)
= 154 cm2
Area of the semicircle = (1/2) × (22/7) × 7√2 × 7√2
= 154 cm2
Area of the shaded region =Area of the semicircle + Area of ΔABC – Area of quadrant
= 154 +98 - 154 cm2
= 98cm2