Answer :

Given. PQRS is a trapezium.

PQ = 4.5 cm, QR = 2.5 cm, RS = 3 cm and SP = 2 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 4.5cm

Step 2 : Mark a point E on PQ such that PE = 3cm and EQ = 1.5cm

Step 3 : Make arc of 2.5cm from point Q and 2cm from point E

Step 4 : Mark the intersecting point of both arcs to be R and join RE and EQ.

Step 5 : Draw arcs of 3cm and 2cm 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 E

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

= × RE × (PQ + SR)

= × 2cm × (4.5cm + 3cm)

= 7.5cm^{2}

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

7.5cm^{2}

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