In the adjoining figure ABCD is a square with sides of length 6 units points P & Q are the mid points of the sides BC & CD respectively. If a point is selected at random from the interior of the square what is the probability that the point will be chosen from the interior of the triangle APQ.

Ans:    Area of triangle PQC = 1/2 x 3 x 3 =  9 = 4. 5 units

Area of triangle ABP = 1/2 x 6 x 3 = 9

Area of triangle ADQ = 1/2 x 6 x 3 = 9

Area of triangle APQ = Area of a square - (Area of a triangle PQC + Area of triangle ABP + Area of triangle ABP)

= 36 - (18+4.5)

= 36 - 22.5

= 13.5

Probability that the point will be chosen from the interior of the triangle APQ = 13.5/36

= 135/360 = /8