Perimeter of a Parallelogram

Perimeter of a Parallelogram, This article will include all the things basic to the problem practice all the things we shall be covering. We shall try to find the answers of some questions like what is perimeter , what do you understand by parallelogram , what are the ways to determine perimeter of parallelogram , then we shall cover the problems along with the solutions and then we shall discuss some Frequently asked questions (FAQs).

In Geometry, the word Perimeter is used as the indicator of the path or length. The word Perimeter originated from two Greek words "PERI" (which means around) and "METER"(which means measure) means measurement of all around the path. 

A perimeter is a length which encompasses/surrounds a two-dimensional or planner shape. The term can be used either for the path, or its length—in a single dimension system. It can be visualized as the length of the boundary of a shape. The perimeter of a circle or ellipse is usually called its circumference.

Let's Recall the Parallelogram !!

In Euclidean geometry, a parallelogram is like a simple quadrilateral which contains two pairs of Parallel sides. The opposite facing sides or Parallel pair sides of a parallelogram are of equal length and the opposite facing angles (as angle BAC = angle BCD in below figure) of a parallelogram are of equal measure.

Example :

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Properties of Parallelogram : 

• Opposite facing parallel sides are congruent (AB = DC).

• Opposite facing angles are Equal (D = B).

• Consecutive Two angles are supplementary (i.e. A + D = 180°).

• If one angle is right, then all angles will be right.

• The diagonals of a parallelogram will be bisected to each other.

• Both the diagonals of a parallelogram separate it into two congruent triangles.

Perimeter of Parallelogram

A Perimeter of any figure can be defined in various mentioned ways.

1. A Perimeter of any polygon is the total length along the outside of the same polygon. 

2. A Perimeter of any figure is the total length of all its sides.

3. A Perimeter is the length of the boundary or length of line of separation of shape with the surrounding.

4. A Perimeter is the measurement of the length of the outline of a shape.

Determining the Perimeter has many practical applications. For example, it could be used to find out the number of revolutions of a wheel, length of a fence surrounding a yard or garden, the amount of wool wound around a spool will also be related to the perimeter of the spool, the distance ran by a runner around a path, etc.

Let “a” and “b” are the sides of a parallelogram. then, the perimeter of a parallelogram formula will be as follows:

We already know that the opposite face sides of a parallelogram are parallel and also equal to each other. Thus, the formula for determining the perimeter of a parallelogram will be given by:

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 will be 2(a+b) units

Perimeter of a Parallelogram with Base(b) and Height(h)

Let us assume a parallelogram with base and height is given. If “b” is the base length of the parallelogram and “h” is the height length of the parallelogram, then the formula will be derived as follows:

According to the properties of the parallelogram, the opposite face sides are parallel and also equal to each other, so the parallelogram perimeter will be determined as two times of sum of the base and height.

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Thus, the formula for the perimeter of a parallelogram will be given by:

P = 2 (b +h/cos θ)

where θ is the mentioned angle BAE, which is formed between the height and side of the parallelogram, i.e. AE and AB.

Problems with Solutions

Example 1:

Determine the perimeter of a parallelogram with the base and side lengths of 10cm and 5cm, respectively.

Solution:

Given:

Base length of a parallelogram = 10 cm

Side length of a parallelogram = 5 cm

We already  know that the perimeter of a parallelogram is given by, P = 2(a+b) units.

Substitute the values

P = 2(10+5)

P = 2(15)

P = 30 cm

Therefore, the perimeter of a parallelogram will be 30 cm.

Example 2:

Determine the length of another side of the parallelogram whose base is 5 cm and the perimeter is 40 cm.

Solution:

Given:

Base, h = 5cm

Perimeter, p = 40cm

We already  know that the perimeter of a parallelogram is given by, P = 2(a+b) units.

Now substitute the given values in the formula,

40 = 2 (a +5)

40 = 2a + 10

2a = 40-10

2a = 30

a = 30/2

a = 15 cm

Thus, the length of the other side of the parallelogram will be 15 cm.