Parallelogram

Area of Parallelogram Using Sides

Suppose a and b are the set of parallel sides of a parallelogram and h is the height, then based on the length of sides and height of it, the formula for its area is given by:

Area = Base × Height

A = b × h [sq.unit]

Example: If the base of a parallelogram is equal to 5 cm and the height is 3 cm, then find its area.

Solution: Given, length of base=5 cm and height = 3 cm

As per the formula, Area = 5 × 3 = 15 sq.cm

Area of Parallelogram Without Height

If the height of the parallelogram is unknown to us, then we can use the trigonometry concept here to find its area.

Area = ab sin (x)

Where a and b are the length of parallel sides and x is the angle between the sides of the parallelogram.

Example: The angle between any two sides of a parallelogram is 90 degrees. If the length of the two parallel sides is 3 cm and 4 cm respectively, then find the area.

Solution: Let a = 3 cm and b=4 cm

x = 90 degrees

Area = ab sin (x)

A = 3 × 4 sin (90)

A = 12 sin 90

A = 12 × 1 = 12 sq.cm.

Note: If the angle between the sides of a parallelogram is 90 degrees, then it is a rectangle.

Area of Parallelogram Using Diagonals

The area of any parallelogram can also be calculated using its diagonal lengths. As we know, there are two diagonals for a parallelogram, which intersects each other. Suppose, the diagonals intersect each other at an angle y, then the area of the parallelogram is given by:

Area = ½ × d1 × d2 sin (y)

To know more about solving the area of a parallelogram, please visit the following links:

https://youtu.be/t42sLuns4Qs

https://youtu.be/uj6k22WubCk