In the Fig. below, JKLM is a square with sides of length 6 units. Points A and B are the

mid- points of sides KL and LM 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 ΔJAB?

#### Solution

**Given:** JKLM is a square with sides of length 6units. Points A* *and B are the midpoints of sides KL and ML respectively. If a point is selected at random from the interior of the square

**To find:** Probability that the point will be chosen from the interior of ΔJAB.

We the following figure

Area of square JLKM is equal to

= `6^2`

= 36 sq units

Now we have

`area(triangleKAJ)= 1/2xxAKxxKJ`

`=1/2xx3xx6`

=9 units^{2}

`area(triangleJMB)=1/2xxJMxxBM`

`=1/2xx6xx3`

=9/2 units^{2}

Now area of the triangle AJB

`area(triangleAJB) = 36-9-9-9/2`

=`27/2`units^{2}

We know that Probability

=`"Number of favourable event"/"Total number of event"`

`= (27/2)/36`

`= 27/(2xx36)`

`= 3/8`

Hence the Probability that the point will be chosen from the interior of ΔAJB is `3/8`.