In the given figure, OACB is a quadrant of a circle with center O and radius 3.5 cm. If OD = 2 cm, find the area of the shaded region.
Given: Radius of the quadrant = r = 3.5 cm
∴ Area of the quadrant = (1/4)πr2
= (1/4) × (22/7) × 3.5 × 3.5
= 9.625 cm2
Given: Height of triangle OBD = OD = 2 cm
Also, Base of triangle OBD = Radius of the quadrant = r = 3.5 cm
∴ Area of the triangle = 1/2 × Base × Height
= 1/2 × 2 × 3.5
= 3.5 cm2
Area of the shaded region = Area of quadrant – Area of right angled triangle OBD = (9.625 – 3.5) cm2 = 6.125 cm2
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