Question

Parallelogram with adjacent sides 6.5 centimetres and 4 centimetres, angle between them 45°.

Answer 1

Let ABCD be the required parallelogram.

Given: DC = AB = 6.5 cm

AD = BC = 4 cm

∠ADC = 45°

Here is the rough sketch of the required parallelogram.

The steps of construction are as follows:

(1) Draw a line segment DC of length 6.5 cm.

(2) At point D, draw ∠XDC of measure 45°.

(3) Taking D as the centre and 4 cm as the radius, draw an arc which intersects ray DX at point A.

(4) Taking A as the centre and 6.5 cm as the radius, draw an arc on the right side of point A.

(5) Taking C as the centre and 4 cm as the radius, draw an arc which intersects the previously drawn arc at point B.

(6) Join AB and BC.

ABCD is the required parallelogram.