Answer :

Given. ABCD is a isosceles trapezium.

AB = 9 cm, DC = 6 cm and AD = BC = 5 cm.

Formula used. Area of trapezium = × height × sum of parallel sides

Area of trapezium = × height × (AB + CD)

Steps of Construction

Step 1 : Draw a line AB of 9cm

Step 2 : Mark a point E on AB such that AE = 6cm and EB = 3cm

Step 3 : Make arc of 5cm from both point E and B

Step 4 : Mark the intersecting point of both arcs to be C and join EC and BC.

Step 5 : Draw arcs of 6cm and 5cm from point C and A respectively

Step 6 : Mark the intersection point of both arcs as D

Step 7 : Join AD and CD to form trapezium ABCD

Step 8 : Draw a perpendicular on AB from point C and name then intersection point as F

Area of trapezium = × height × (AB + CD)

= × CF × (AB + CD)

= × 4.7cm × (9cm + 6cm)

= 35.25cm^{2}

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

35.25cm^{2}

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