Question

Construct a trapezium ABCD, in which $AD\parallel BC$ and AD = 3.0 cm, AB = 2.5 cm, BC = 5.0 cm and CD = 2.8 cm. [4 MARKS]

Answer 1

Concept : 1 Mark
Steps : 1 Mark
Construction : 2 Marks

Concept :
In trapezium ABCD, $AD\parallel BC$. A trapezium can be divided into a parallelogram ABED and a triangle DEC.
AB = DE [Opposite sides of a parallelogram]

Steps of construction :

1. Construct a line segment of BC.
2. Divide BC into two parts as BE = 3cm and EC = 2cm.
3. Taking B as the centre, draw an arc of 2.5cm.
4. Taking E as the centre, draw an arc of 2.5cm and taking C as centre draw an arc of 2.8cm which intersects the previous arc at point D.
5. Taking D as the center, draw an arc of 3cm. which intersect arc from B at A
6. Join AB and AD.
7. ABCD is your required trapezium.