Question

M is a point on side PQ of rectangle PQRS. SR is produced to a point N and MSRT is a parallelogram. PQ = 8.5 cm, PS = 6 cm. Find the area of

1. parallelogram MSRT
2. ΔMNT

Answer 1

Given:

• PQ = 8.5 cm 
• PS = 6 cm
• MSRT is a parallelogram
• M is a point on side PQ
• SR is produced to a point N
• We need to find the area of parallelogram MSRT and triangle MNT.

Step-by-step approach:

1. Understanding the problem:

The parallelogram MSRT is formed such that MS || RT and SR || MT.

The point N lies on the extension of line SR.

The area of the parallelogram MSRT can be calculated using the formula for the area of a parallelogram:
Area of parallelogram = Base × Height

The base will be the length of side SR and the height will be the perpendicular distance between lines SR and MT.

2. Finding the area of parallelogram MSRT:

The area of parallelogram MSRT is given by:
Area of MSRT = PQ × PS

Substituting the given values:

Area of MSRT = 8.5 × 6

= 51 cm²

3. Finding the area of triangle MNT:

Since triangle MNT is half of parallelogram MSRT (because the area of a triangle formed by one of the diagonals of a parallelogram is half of the parallelogram’s area), we can calculate its area as:

Area of triangle = `1/2` × Area of parallelogram

Substituting the area of parallelogram MSRT:

Area of triangle MNT = `1/2` × 51

= 25.5 cm²