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

is parallel to PQ = 6.5 cm,QR = 7 cm,∠PQR = 85°,PS = 9cm

Given. PQRS is a trapezium.

PQ = 6.5 cm, QR = 7 cm, PS = 9 cm , ∠ PQR = 85°

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 6.5cm

Step 2 : Make an angle of 85° from point Q and extend ray to QR’

Step 3 : Mark an arc of 7cm 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 9cm on ray RS’ from point P and name intersection point as 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)

= × 7cm × (6.5cm + 11.8cm)

64.05cm²

Conclusion. Hence; Trapezium PQRS is constructed and its area is 64.05cm²