MathMaster Blog

A parallelogram is a four-sided, two-dimensional figure with the following properties:

• two equal and opposing sides
• two intersecting but non-equal diagonals, and
• two equal and opposite angles

#1:

A parallelogram's area is calculated by multiplying its base by its altitude. The base and altitude of a parallelogram are perpendicular to each other.

#2:

If the length of neighboring sides and the angle between them are known, the area of a parallelogram can be determined without the height. In this case, we can use the area of the triangle formula from the trigonometry concept:

Area = ab sin (θ)

Where:

a and b = length of parallel sides, and,

θ = angle between the sides of the parallelogram

#3:

The length of a parallelogram's diagonals can also be used to calculate its area.

Area = ½ x d1x d2sin(x)

Where:

d1 and d2 = length of the diagonals, and,

x = angle between the diagonals

Example 1:

Calculate the area of a parallelogram with 18 cm and 15 cm diagonals and a 43° angle of intersection between them.

Solution:

Let d1 = 18 cm and d2 = 15 cm.

β = 43°

A = ½ x d1 x d2 sine (β)

= ½ x 18 x 15 sine (43°)

= 135 sine (43°)

= 92.07 cm2

Answer: The area of the parallelogram is 92.07 cm^2

Example 2:

Calculate the height of a parallelogram with parallel sides of 30 cm and 40 cm and a 36-degree angle between them. Assume that the parallelogram's base is 40 cm.

Solution:

Area = ab sine (a) = bh

30 x 40 sine(36) = 40 x h

1.200 sine(36) = 40 x h

Divide both sides by 40.

h = (1200/40) sine 36

= 30 sine 36

h = (1200/40) sine 36

= 30 sine 36

h = 17.63 cm

Answer: The height of the parallelogram is 17.63 cm.