Height Of A Parallelogram Formula
Height of A Parallelogram Formula
The Height Of A Parallelogram Formula is used to find the height of a parallelogram. The Height Of A Parallelogram Formula is the perpendicular distance between the base of the parallelogram and the parallel sides. Students must take a look at the Height Of A Parallelogram Formula equation, along with the example which has been solved on the Extramarks website.
What is Height of a Parallelogram Formula?
The height of a parallelogram can be calculated using its area formula, which states that the area of a parallelogram is equal to the product of its base length and height. This formula can be rearranged to solve for the height by dividing the area by the length of the base. Essentially, the height of a parallelogram formula is derived from its area formula, providing a convenient method for determining the height when the area and base length are known.
Height of Parallelogram Formula
Since, Area = Base × Height
Height = Area/Base
Perimeter of a Parallelogram
In a parallelogram, the perimeter, denoted by P, is calculated by adding the lengths of all four sides. Since opposite sides of a parallelogram are equal in length, we can represent the lengths of the opposite sides as X and Y. Therefore, the perimeter can be expressed as:
P = X+Y+X+Y = 2X+2Y = 2(X+Y)
So, the perimeter of a parallelogram can be written as 2(X+Y).
Solved Examples on Height of a Parallelogram Formula
Example 1: Suppose we have a parallelogram with a base of length 6 units and an area of 24 square units. Calculate the height of the parallelogram.
Solution:
Given,
Area (A) = 24 square units
Base (b) = 6 units
Using the formula for the height of a parallelogram:
h = A/b
=24/6
=4
Therefore, the height of the parallelogram is 4 units.
Example 2: Suppose a parallelogram has a base of length 10 cm and a height of 8 cm. Calculate the area of the parallelogram.
Solution:
Given,
Base (b) = 10 cm
Height (h) = 8 cm
Using the formula for the area of a parallelogram:
A = b×h = 10×8 = 80
Therefore, the area of the parallelogram is 80 square cm.
Example 3: Suppose the area of a parallelogram is 45 square units and its height is 5 units. Calculate the length of its base.
Solution:
Given,
Area (A) = 45 square units
Height (h) = 5 units
Using the formula for the base of a parallelogram:
b=A/h
=45/5
=9
Therefore, the length of the base of the parallelogram is 9 units.
Examples Using Height Of A Parallelogram Formula
Examples of using the Height Of A Parallelogram Formula are provided henceforth.
Example 1: Calculate the height of a parallelogram with a base length of 24 units and a parallelogram area of 144 square units.
Solution:
Given that:
Area = 144
base = 24
Use the Height Of A Parallelogram Formula
Parallelogram height = area/base length
Height = 144/24
height = 6 units
Answer: The parallelogram is 6 units high.
Example 2: If the side of a diamond is 12 inches and the area of the diamond is 120 square inches, what is the height of the diamond?
Solution:
Given that:
Area = 120
base = 12
A rhombus is a special case of a parallelogram, so students can find its height using the parallelogram height formula:
Parallelogram height = area/base length
Height = 120/12
height = 10 units
Answer: A diamond is 10 units high.
Example 3: Suppose a parallelogram has a base of length 10 cm and a height of 8 cm. Calculate the area of the parallelogram.
Solution:
Given,
Base (b) = 10 cm
Height (h) = 8 cm
Using the formula for the area of a parallelogram:
A = b×h = 10×8 = 80
Therefore, the area of the parallelogram is 80 square cm.
FAQs (Frequently Asked Questions)
1. What is a parallelogram?
A parallelogram is a four-sided geometric object consisting of two pairs of parallel lines. In a parallelogram, opposite sides have equal lengths and opposite angles have equal angles.
2. How to find the area of a parallelogram?
The area of a parallelogram will always be calculated using the formula:
Area = base area x height. There are also other methods mentioned in the article that can be used to find the area of a parallelogram.
3. What is the parallelogram perimeter?
To find the perimeter of a parallelogram, sum all the sides to get the answer. The given formula gives the perimeter of a given parallelogram.
Perimeter = 2 (a + b)
where a and b are the side lengths of the parallelogram.
4. What is the purpose of base and height in a Parallelogram?
In parallelogram “Base” indicates the length of a side and “Height” is the length of a perpendicular between two parallel lines.
