Question

Area of parallelogram PQRS is 64 cm² and PR = 10 cm. If ST is perpendicular to PR, find the length of ST.

Answer 1

Given:

• Area of parallelogram PQRS = 64 cm²
• Diagonal PR = 10 cm
• ST is perpendicular to PR

Step-wise calculation:

1. The diagonal PR divides the parallelogram into two congruent triangles, so the area of triangle PSR is half of the area of parallelogram PQRS.

Area of ΔPSR = `1/2 xx 64`

= 32  cm²

2. The area of triangle PSR can also be expressed as:

Area of ΔPSR = `1/2 xx PR xx ST`

3. Substitute the known values area = 32 cm², PR = 10 cm into the area formula:

`32 = 1/2 xx 10 xx ST`

4. Simplify and solve for ST: 

32 = 5 × ST

ST = `32/5` 

= 6.4  cm

Length of ST is 6.4 cm.