Geometry is a branch of Mathematics that deals with the study of different geometrical shapes. It is of two types:
- Two-dimensional Geometry
- Three-dimensional Geometry
A parallelogram is a two-dimensional geometric shape bounded by four sides. The pair of opposite sides of a parallelogram are parallel and equal to each other. A parallelogram is slightly different from a rectangle in terms of vertical angles. In a rectangle, the measure of the vertical angle is 90°. But in a parallelogram, it is not necessarily equal to 90°.
How to Calculate the Perimeter of a Parallelogram?
The perimeter is defined as the length of the boundaries of any shape. The sum of all the sides of a parallelogram is known as the perimeter of a parallelogram.
Perimeter of a Parallelogram Formula
Let “a” and “b” be the sides of a parallelogram. Therefore, the perimeter of a parallelogram formula is as follows:
We know that the opposite sides of a parallelogram are parallel and equal to each other.
So, the perimeter of Parallelogram, P = a + b + a + b units
P = 2a +2b
P = 2(a+b)
Therefore, the perimeter of a parallelogram, P = 2(a+b) units
Relation Between Area and Perimeter of a Parallelogram
We know that the area of a parallelogram is equal to the product of base and height.
A = b x h square units. —-(1)
The relationship between the area and perimeter of a parallelogram is:
P = 2 (a+b) units
Therefore, the value of b in terms of P is
P/2 = a + b
b=(P/2) – a
Now, substitute the value of b in (1)
A = ((P/2) – a)h Square units
Example
Question:
Find the perimeter of a parallelogram whose base and height are 10cm and 5cm, respectively.
Solution:
Given:
Base of a parallelogram = 10 cm
Height of a parallelogram = 5 cm
We know that the perimeter of a parallelogram, P = 2(a+b) units
Substitute the values
P = 2(10+5)
P = 2(15)
P = 30 cm
Therefore, the perimeter of a parallelogram is 30 cm
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