How to Calculate the Perimeter of a Parallelogram with Examples
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 :
[Image will be Uploaded Soon]
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.
A Perimeter of any polygon is the total length along the outside of the same polygon.
A Perimeter of any figure is the total length of all its sides.
A Perimeter is the length of the boundary or length of line of separation of shape with the surrounding.
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.
[Image will be Uploaded Soon]
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.
FAQs on Perimeter of a Parallelogram Explained
1. What exactly is the perimeter of a parallelogram?
The perimeter of a parallelogram is the total length of the boundary enclosing the shape. Imagine walking along all four sides of a parallelogram; the total distance you cover is its perimeter. It is a one-dimensional measurement, expressed in units like centimetres (cm) or metres (m).
2. What is the formula used to calculate the perimeter of a parallelogram?
The formula to calculate the perimeter of a parallelogram is P = 2(a + b), where 'a' and 'b' are the lengths of the two adjacent sides. Since opposite sides of a parallelogram are equal in length, you can also find the perimeter by adding the lengths of all four sides: P = a + b + a + b.
3. How do you find the perimeter of a parallelogram with an example?
To find the perimeter, you only need the lengths of two adjacent sides. For example, if a parallelogram has adjacent sides of 8 cm and 6 cm, you can calculate its perimeter using the formula P = 2(a + b).
- P = 2 (8 cm + 6 cm)
- P = 2 (14 cm)
- P = 28 cm
4. How can you find the length of a missing side of a parallelogram if the perimeter and one side are known?
If you know the perimeter (P) and the length of one side (a), you can find the adjacent side (b) by rearranging the formula. The formula is P = 2(a + b). To find 'b', you can use: b = (P/2) - a. For instance, if the perimeter is 30 cm and one side is 10 cm, the adjacent side would be (30/2) - 10 = 15 - 10 = 5 cm.
5. What is the key difference between the perimeter and area of a parallelogram?
The primary difference lies in what they measure.
- Perimeter is the measure of the boundary or the total length of the sides of the parallelogram. It is a linear measurement (e.g., in metres).
- Area is the measure of the surface or space enclosed within that boundary. It is a two-dimensional measurement (e.g., in square metres).
6. Why is the perimeter formula for a parallelogram, P = 2(a + b), the same as the formula for a rectangle?
The perimeter formula is the same because both a parallelogram and a rectangle are quadrilaterals with two pairs of equal-length opposite sides. The concept of perimeter is simply the sum of all side lengths. Since both shapes have sides of lengths 'a', 'a', 'b', and 'b', the total sum for both is 2a + 2b, which simplifies to 2(a + b). The difference between them (the angles) affects the area, but not the total length of the boundary.
7. Can you give a real-world example where calculating the perimeter of a parallelogram is important?
A common real-world example is in construction or fencing. If you need to build a fence around a garden plot that has the shape of a parallelogram, you would need to calculate its perimeter to determine the total length of fencing material required. Similarly, it's used in design to frame a parallelogram-shaped window or a piece of art.
8. Do you need the height of a parallelogram to find its perimeter?
No, you do not need the height to calculate the perimeter. This is a common point of confusion. The height of a parallelogram is the perpendicular distance between its base and the opposite side, and it is essential for calculating the area (Area = base × height). The perimeter only depends on the lengths of the two adjacent sides.
9. If two parallelograms have the same perimeter, must they also have the same area?
Not necessarily. Two parallelograms can have the exact same perimeter but vastly different areas. For example, a long, thin parallelogram and a more 'upright' one (closer to a rectangle) can be made with the same side lengths. The one with angles closer to 90 degrees will have a greater height and therefore a larger area, even though their perimeters are identical.
