Parallelogram with Four Equal Sides

In geometry, a parallelogram is a quadrilateral with the two pairs of parallel sides. In Euclidean Geometry, the opposites or facing sides of a parallelograms are of equal length and the opposite angles of a parallelogram are of equal measure. The congruences of opposite sides and opposite angles are a direct consequence of the Euclidean Parallel Postulate and neither condition can be proven without appealing to the Euclidean Parallel Postulate or one of its equivalent formulations. The three-dimensional counterparts of a parallelogram is a parallelepiped.(Source.Wikipedia)

Parallelogram with Equal Sides are Square and Rhombus:

Parallelograms:

Area of parallelograms A = b *  h   sq. units



where h is the perpendicular height of the parallelogram.

b is the base length of the parallelogram.

Examples for Parallelogram with Equal Sides:

Example 1:

Find the area of the rhombus whose base is 150cm and the perpendicular height will be equal to 150cm.

Given:

H=150cm

B=150cm

Solution:

Area = b*h

= 150*150

= 22500cm2

Example 2:

Find the Area of a Parallelogram with a base of 12 centimeters and a height of 15 centimeters.

Solution:

A=b*h

A= (12 cm) · (15 cm)

A= 180 cm2

Example 3:

Find the area of a parallelogram with a base of 8 inches and a height of 14 inches.

Solution:

A=b*h

A= (8 in) · (14 in)

A= 112 in2

Example 4:

The area of a parallelogram is 30 square centimeters and the base is 60 centimeters. Find the height.

Solution:

A=b*h

30 cm2 = (60 cm) · h

30 cm2 ÷ (60 cm) = h

h= 0.5 cm

Example 5:

The area of a parallelogram is 100 square centimeters and the base is 50 centimeters. Find the height.

Solution:

A=b*h

100 cm2 = (50 cm) · h

100 cm2 ÷ (50 cm) = h

h= 2 cm.

These are the examples on parallelogram with four equal sides.