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Question

Construct a trapezium ABCD in which ¯¯¯¯¯¯¯¯AB is parallel to ¯¯¯¯¯¯¯¯¯DC , AB = 10 cm,BC = 5 cm, AC = 8 cm and CD = 6 cm. Find its area.

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Solution

Given:
¯¯¯¯¯¯¯¯AB is parallel to ¯¯¯¯¯¯¯¯¯DC, AB = 10 cm, BC = 5 cm, AC = 8 cm and CD = 6 cm.

Steps for construction:
Step 1 : Draw a rough diagram and mark the given measurements.
Step 2 : Draw a line segment AB = 10 cm.
Step 3 : With A and B as centres draw arcs of radii 8 cm and 5 cm respectively and let them cut at C.
Step 4 : Join
¯¯¯¯¯¯¯¯AC and ¯¯¯¯¯¯¯¯BC .
Step 5 : Draw
¯¯¯¯¯¯¯¯¯CX parallel to ¯¯¯¯¯¯¯¯BA .
Step 6 : With C as centre and radius 6 cm draw an arc cutting
¯¯¯¯¯¯¯¯¯CX at D.
Step 7 : Join ¯¯¯¯¯¯¯¯¯AD . ABCD is the required trapezium.
Step 8 : From C draw ¯¯¯¯¯¯¯¯CE¯¯¯¯¯¯¯¯AB and measure the length of CE. CE = h = 4 cm. AB = a = 10 cm, DC = b = 6 cm.
Calculation of area:
In the trapezium ABCD, a = 10 cm, b = 6 cm and h = 4 cm.
Area of the trapezium ABCD = 12 h(a+b)

=12 (4)(10+6)

=12× 4 × 16

=32cm2

754775_616727_ans_ee59555c39914921b8e9815d7cb30e36.png

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