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

is parallel to PQ = 8 cm, QR = 5 cm,RS = 6 cm,SP = 4 cm

Given. PQRS is a trapezium.

PQ = 8 cm, QR = 5 cm, RS = 6 cm and SP = 4 cm

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 8cm

Step 2 : Mark a point E on PQ such that PE = 6cm and EQ = 2cm

Step 3 : Make arc of 5cm from point Q and 4cm from point E

Step 4 : Mark the intersecting point of both arcs to be R and join ER and RQ

Step 5 : Draw arcs of 6cm and 4cm from point R and P respectively

Step 6 : Mark the intersection point of both arcs as S join SP and RS

Step 8 : Draw a perpendicular on PQ from point R and name the intersection point as F

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

= × RF × (PQ + SR)

= × 3.8cm × (8cm + 6cm)

= 26.6cm²

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

26.6cm²