Rhombus with side 4 centimetres, angle between sides 30°.

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Solution

Let ABCD be the required rhombus.

Given: AB = BC = CD = DA = 4 cm

∠ADC = 30°

Here is the rough sketch of the required rhombus.

The steps of construction are as follows:

(1) Draw a line segment DC of length 4 cm.

(2) At point D, draw ∠XDC of measure 30°.

(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 4 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 rhombus.

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