In the adjoining figure a dart is thrown at the dart board and lands in the interior of the circle. What is the probability that the dart will land in the shaded region.

Ans: We have

AB = CD = 8 and AD = BC = 6

using Pythagoras Theorem is ? ABC, we have

AC² = AB² + BC²

AC² = 8² + 6² = 100

AC = 10

OA = OC = 5  [ Q O is the midpoint of AC]

∴      Area of the circle = π (OA)² = 25  π sq units [Q Area = π r²]

Area of rectangle ABCD = AB x BC = 8 x 6 = 48 sq units

Area of shaded region = Area of the circle - Area of rectangle ABCD Area of shaded region = 25 π - 48 sq unit.

Hence P (Dart lands in the shaded region) = Area of shaded region/Area of circle =     25π - 48/25π