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

is parallel to PQ = 7 cm, ∠Q = 60°,QR = 5 cm RS = 4 cm.

Given. PQRS is a trapezium.

PQ = 7 cm, QR = 5 cm and RS = 4 cm , ∠Q = 60°

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 7cm

Step 2 : Make an angle of 60° from point Q and extend ray to QR’

Step 3 : Mark an arc of 5cm from Q on ray QR’ and name intersection point as R

Step 4 : Draw a ray RS’ parallel to PQ from point R

Step 5 : Make arc of 4cm on ray RS’ from point R and name intersection point S

Step 6 : Join point S and P to form trapezium PQRS

Step 7 : Draw a perpendicular on PQ from point R and name the intersection point as E

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

= × RE × (PQ + SR)

= × 4.3cm × (7cm + 4cm)

= 23.65cm²

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

23.65cm²