Find Perimeter Of Parallelogram Calculator

Calculate Perimeter

Perimeter Variation Chart

Chart showing how the perimeter changes when one side length is varied while the other is kept constant around the input values.

What is the Perimeter of a Parallelogram?

The perimeter of a parallelogram is the total distance around the outside of the parallelogram. It's the sum of the lengths of its four sides. Since opposite sides of a parallelogram are equal in length, if we know the lengths of two adjacent sides (let's call them 'a' and 'b'), we can easily find the perimeter.

This calculator is useful for students learning about geometry, architects, engineers, or anyone needing to calculate the boundary length of a parallelogram-shaped area. Common misconceptions include confusing the perimeter with the area or using the height instead of the side length for perimeter calculation.

Perimeter of a Parallelogram Formula and Mathematical Explanation

The formula to find the perimeter of a parallelogram is:

P = 2 * (a + b)

Where:

• P is the Perimeter of the parallelogram.
• a is the length of one side.
• b is the length of an adjacent side.

The formula works because a parallelogram has two pairs of equal-length sides. So, if two adjacent sides have lengths 'a' and 'b', the other two sides also have lengths 'a' and 'b'. The total perimeter is a + b + a + b = 2a + 2b = 2(a + b).

Variables Table

Variable	Meaning	Unit	Typical Range
P	Perimeter	Length (e.g., cm, m, inches)	Positive
a	Length of one side	Length (e.g., cm, m, inches)	Positive
b	Length of adjacent side	Length (e.g., cm, m, inches)	Positive

Variables used in the perimeter of a parallelogram formula.

Practical Examples (Real-World Use Cases)

Let's look at some examples of calculating the perimeter of a parallelogram.

Example 1: Fencing a Garden Plot

Imagine you have a garden plot shaped like a parallelogram with adjacent sides measuring 8 meters and 12 meters.

• Side a = 8 m
• Side b = 12 m
• Perimeter P = 2 * (8 + 12) = 2 * 20 = 40 meters.

You would need 40 meters of fencing to enclose the garden.

Example 2: Framing a Picture

A picture frame is in the shape of a parallelogram with sides of 30 cm and 45 cm.

• Side a = 30 cm
• Side b = 45 cm
• Perimeter P = 2 * (30 + 45) = 2 * 75 = 150 cm.

The total length of the material needed for the frame is 150 cm.

How to Use This Perimeter of a Parallelogram Calculator

1. Enter Side 'a': Input the length of one side of the parallelogram into the "Length of Side 'a'" field.
2. Enter Side 'b': Input the length of the adjacent side into the "Length of Side 'b'" field.
3. Calculate: The calculator automatically updates the results as you type. You can also click the "Calculate" button.
4. View Results: The "Perimeter (P)" will be displayed prominently, along with intermediate calculations.
5. Reset: Click "Reset" to clear inputs and results to default values.
6. Copy: Click "Copy Results" to copy the inputs, perimeter, and formula to your clipboard.

The results section clearly shows the calculated perimeter of a parallelogram based on your inputs.

Key Factors That Affect Perimeter of a Parallelogram Results

The perimeter of a parallelogram is directly affected by:

1. Length of Side 'a': As the length of side 'a' increases (or decreases), the perimeter increases (or decreases) proportionally, assuming side 'b' remains constant.
2. Length of Side 'b': Similarly, as the length of side 'b' increases (or decreases), the perimeter increases (or decreases) proportionally, assuming side 'a' remains constant.
3. Units of Measurement: The units of the perimeter will be the same as the units used for the sides (e.g., cm, meters, inches). Ensure consistency.
4. Accuracy of Measurement: The precision of the perimeter depends on how accurately the side lengths 'a' and 'b' are measured.
5. Angles (Not for Perimeter): The angles of a parallelogram affect its area and the length of its diagonals, but not its perimeter, which only depends on the side lengths.
6. Shape: If the shape is not a parallelogram (i.e., opposite sides are not equal), this formula won't apply directly.

Frequently Asked Questions (FAQ)

Q: What is a parallelogram?

A: A parallelogram is a quadrilateral (a four-sided polygon) with two pairs of parallel and equal-length sides.

Q: How do I find the perimeter of a parallelogram if I only know one side and the height?

A: You cannot find the perimeter with only one side and the height. The height is used for area calculation. You need the lengths of two adjacent sides (a and b) for the perimeter.

Q: Is a rectangle a parallelogram?

A: Yes, a rectangle is a special type of parallelogram where all angles are 90 degrees.

Q: Is a square a parallelogram?

A: Yes, a square is a special type of parallelogram (and also a special rectangle and rhombus) where all sides are equal, and all angles are 90 degrees.

Q: What's the difference between perimeter and area of a parallelogram?

A: The perimeter is the total length of the boundary (P=2(a+b)), while the area is the space enclosed within the boundary (Area = base * height).

Q: If I double the sides of a parallelogram, what happens to the perimeter?

A: If you double both side 'a' and side 'b', the new perimeter will be 2 * (2a + 2b) = 4(a + b), which is double the original perimeter.

Q: Can I use this calculator for a rhombus?

A: Yes, a rhombus is a parallelogram with all four sides equal. So, if you enter a=b, the formula P=2(a+a)=4a will give the correct perimeter.

Q: Do the angles of a parallelogram affect its perimeter?

A: No, the perimeter depends only on the lengths of the sides (a and b), not the angles between them.