How To Find The Height Of A Parallelogram With Formulas - Math Monks

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What is the Height of a Parallelogram

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. fth = 36/4h4h2 = 36h2 = 36/4h = 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

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