Construct trapezium PQRS with the following measurements. Find also its area.

is parallel to PQ = 6 cm, PS = 5 cm, ∠QPS = 60° and ∠PQR = 100°.

Given. PQRS is a trapezium.

PQ = 6 cm, PS = 5 cm , ∠QPS = 60° and ∠PQR = 100°

Formula used. Area of trapezium = × height × sum of parallel sides

Area of trapezium = × height × (PQ + SR)

Steps of Construction

Step 1 : Draw a line PQ of 6cm

Step 2 : Make an angle of 100° from point Q and extend ray to QR’

Step 3 : Make an angle of 60° from point P and extend ray to PS’

Step 4 : Mark an arc of 5cm from P on ray PS’ and name intersection point as S

Step 5 : Draw a ray SR” parallel to PQ from point S

Step 6 : Mark the intersection point of SR” and QR’ as R

Step 7 : Draw a perpendicular on PQ from point S and name the intersection point as A

Area of trapezium = × height × (PQ + SR)

= × SA × (PQ + SR)

= × 4.3cm × (6cm + 4.3cm)

= 22.145cm²

Conclusion. Hence; Trapezium PQRS is constructed and its area is

22.145cm²