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

is parallel to PQ = 7.5 cm, PS = 6.5 cm, ∠QPS = 100° and ∠PQR = 45°.

Given. PQRS is a trapezium.

PQ = 7.5 cm, PS = 6.5 cm , ∠QPS = 100° and ∠PQR = 45°.

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 7.5cm

Step 2 : Make an angle of 45° from point Q and extend ray to QR’

Step 3 : Make an angle of 100° from point P and extend ray to PS’

Step 3 : Mark an arc of 6.5cm from P on ray PS’ and name intersection point as S

Step 4 : Draw a ray SR” parallel to PQ from point S

Step 5 : Mark the intersection point of SR” and QR’ as R

Step 6 : Draw a perpendicular on PQ from point R and name the intersection point as E

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

= × RE × (PQ + SR)

= × 6.4cm × (7.5cm + 2.2cm)

= 31.04cm²

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

31.04cm²