The height of a parallelogram is the perpendicular distance between any of its two parallel sides. It is also termed the altitude of a parallelogram. The height of any parallelogram is identified based on the side we choose as its base.
Formulas
There are two ways to find the height of a parallelogram. The formulas are given below
With Base and Height
This is the basic formula to calculate the height of a parallelogram. The formula is obtained from the standard formula of the area of the parallelogram.
Area of a parallelogram (A) = b × h, here b = base, h = height
⇒ h = A/b
This is the formula to calculate the height of a parallelogram
Height of a Parallelogram
Calculate height of a parallelogram whose base is 18 m and area is 162 sq. m.
Solution:
As we know, h = A/b, here A = 162 sq. m, b = 18 m = 162/18 = 9 m
What is the altitude of a parallelogram with a base four times the height with an area of 36 sq ft.
Solution:
As we know, h = A/b, here b = 4h ft (since b is 4 times the h), A = 36 sq. ft h = 36/4h 4h2 = 36 h2 = 36/4 h = 3 ft
Now let us learn how to find the height of a parallelogram when the area is not known.
Without Area
Sometimes, the height of a parallelogram is calculated using an alternative formula, when the area is unknown. It is derived below:
As we know,
Area of a parallelogram (A) = ab sin(θ), here a and b are 2 consecutive sides, θ = vertex angle
Also,
h = A/b
Substituting the value of ‘h’ in the above formula, we get
⇒ h = ab sin(θ)/b
⇒ h = a sin(θ)
Height of a Parallelogram Without Area
Find the altitude of the parallelogram with a side of 15 cm and the angle of 45° between 2 sides.
Solution:
As we know, h = a sin(θ), here a = 15 cm, θ = 45° = 15 × sin(30°) = 15 × 1/2 = 7.5 cm
