We know that, in rhombus all sides are equal. To construct a rhombus whose side is of length 3.4 cm and one of its angle is 45°, use the following steps
1.Draw a line segment AS of length 3.4 cm.
2.Now, generate an angle 45° at both ends A and B of line segment AB and plot the parallel lines AX and BY.
3.Cut AD and SC of length 3.4 cm from AX and BY, respectively.
4.Draw an angle of 45° at one of the point D or C and join both points by a line segment DC of length 3.4 cm and parallel to AB.
Thus, ABCD is the required rhombus whose side is of length 3.4 cm and one of its angle is 45°.
Alternate Method
To construct a rhombus whose side is of length 3.4 cm and one of its angle is 45°, use the following steps.
1.Draw a line segment AB of length 3.4 cm. .
2.Now, draw an angle XAB = 45° at point A of line segment AB.
3.Cut a line segment AD = 3.4 cm from the ray AX and join BD.
4.Now, from D point C is at a distance of 3.4 cm. So, having D as centre draw an arc of radius 3.4 cm.
5.From B, point C is at distance of 3.4 cm. So, having B as centre draw an arc of radius 3.4 cm which intersect previous arc (obtained in step iv) at C.
6.Join CD and BC.
Thus, ABCD is required rhombus whose side is of length 3.4 cm and one of its angle is 45°.