Construct a parallelogram whose diagonal is 5.4 cm and 6.2 and an angle between them is 70.

A parallelogram is a type of quadrilateral in which the opposite sides are parallel and equal.

Answer: The construction of the parallelogram is given below.

Let's follow the steps of construction.

Explanation:

In a parallelogram, the diagonals bisect each other.

The following are the steps of construction to draw a parallelogram ABCD with the given parameters:

• Draw AC = 5.4 cm.
• Construct the perpendicular bisector of AC, i.e., Bisect AC at O.
• Draw ∠COX = 70° and produce XO to Y.
• With O as the center cut an arc OB = 3.1 cm (since 1/2 of the diagonal BD = 1/2 × 6.2 =1.3) and OD = 1/2 × 6.2 =3.1 cm as shown.
• Join AB, BC, CD, and DA.

Thus, the parallelogram ABCD is drawn with lengths of diagonals as 5.4 cm, 6.2 cm respectively.