Question

OAB is a quadrant of a circle of radius 14 cm. A semi-circle is drawn on diameter OB. Calculate (i) the shaded area (ii) length of arc AB.​

Answer 1

Area of shaded region = area of semicircle of diameter BC - {area of quadrant of radius AB /AC - area of ∆ABC }

So, area of semicircle of diameter BC = 1/2 πr²

= 1/2 × 22/7 × 7√2 × 7√2 [ ∵ BC is hypotenuse of right angle ∆ABC , here AB = BC = 14 so, BC = 14√2 = 2 × radius ⇒ radius = 7√2 ]

= 11 × 7 × 2 = 154 cm²

area of quadrant of radius AB/AC = 1/4 πr²

= 1/4 × 22/7 × 14 × 14

= 22 × 7 = 154 cm²

area of ∆ABC = 1/2 height × base

= 1/2 × 14 × 14 = 98 cm²

Now, area of shaded region = 154cm² - { 154cm² - 98cm²} = 98cm²

Hence, area of shaded region = 98 cm²