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

is parallel to PQ = 8 cm,QR = 5 cm, PR = 6 cm,RS = 4.5 cm

Given. PQRS is a trapezium.

PQ = 8 cm, RS = 4.5 cm , QR = 5 cm, PR = 6 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 : Make an arc of 6cm from point P and 5cm from point Q

Step 3 : Mark the intersection point as R and join PR and QR

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

Step 5 : Make an arc of 4.5cm on ray RS’ from point R 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)

= × 3.8cm × (4.5cm + 8cm)

= 23.75cm²

Conclusion. Hence; Trapezium PQRS is constructed and its area is 23.75cm²