Perimeter of Parallelogram - Definition, Formula, and Examples

When forms look alike, a lot of pupils have trouble with geometry. You are in the right place if you are having trouble figuring out how to measure the edge of a four-sided figure that is tilted. This guide makes the perimeter of parallelogram easier to understand by using simple stages, clear graphics, and real-life situations.

What is Perimeter of Parallelogram?

The perimeter of a parallelogram is the total length of the shape's edges. Picture a rectangular field that someone pushed a little to the side, making it lean. That shape is a parallelogram.

A parallelogram is a flat, two-dimensional shape with four sides. Because the opposite sides are identical, finding the perimeter does not require you to measure every single side manually if you already know the length of two adjacent sides.

Properties That Help Calculate Perimeter

To master this, you should remember these specific traits:

• Opposite sides are equal: If the bottom side is 10 cm, the top side is also 10 cm.

• Opposite sides are parallel: They never meet, no matter how far they extend.

• Total Boundary: The perimeter is always a linear measurement (units, not units squared).

Perimeter of Parallelogram Formula

• We apply a certain math rule to figure out how far around the shape is. The formula comes from the fact that a parallelogram has two pairs of sides that are the same length.

• The total distance is: If we let "a" stand for the length of the base and "b" stand for the length of the side next to it, 

• The perimeter is the sum of a and b.

• We can get the conventional formula by making this easier: P = 2(a + b). 

Understanding the Components

The table below shows you what you need to know to utilise the formula correctly:

 Read More - Perimeter of a Circle – Definition, Formula, πd & 2πr with Examples

Perimeter of Parallelogram with Base and Height

A common mistake students make is confusing height with the side length. When looking at the base and height, you must be careful.

The height (h) is the perpendicular distance between the bases. The slanted side (b) is not the same.

• To find the area, you need to know the height.

• Side length is used to calculate perimeter.

Assuming a question gives you the base and height but asks for the perimeter, you need to use the Pythagorean theorem(assuming you have adequate angle information) to get the length of the slanted side, or you can check to see whether the length of the side is already supplied. You can't find the perimeter just by knowing the height and base. You also need to know how long or how steep the slope is.

How to Calculate Perimeter of Parallelogram?

It's easy to understand how to find the perimeter of a parallelogram if you do it in a rational way. This is how it works:

1. Find the Sizes: Look at the number or the problem. Please write down the length of the base (a) and the side next to it (b).

2. Check out the Units: Check that both lengths are in the same unit, such cm or m. If not, switch them.

3. Use this formula: To get the solution, use the formula P = 2 (a + b).

4. First, add the two sides that are inside the brackets.

5. To get the total for all four sides, add the two sides together.

6. Give the outcome a name: Write the final answer using the proper linear unit.

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Perimeter of Parallelogram Examples

The best method to comprehend the perimeter of a parallelogram is to practise it. Let's look at some situations that happen a lot.

Example 1: Basic Calculation

Question: A parallelogram has a base of 12 cm and an adjacent side of 8 cm. Find its perimeter.

• Step 1: Side a = 12 cm, Side b = 8 cm.

• Step 2: Use the formula P = 2 (a + b).

• Step 3: P = 2 (12 + 8).

• Step 4: P = 2 (20).

• Result: P = 40 cm.

Example 2: Finding a Missing Side

Question: The perimeter of the parallelogram is 60 m. If the base is 20 m, what is the length of the other side?

• Step 1: P = 60, a = 20.

• Step 2: 60 = 2 (20 + b).

• Step 3: Divide both sides by 2: 30 = 20 + b.

• Step 4: Subtract 20 from 30.

• Result: b = 10 m.

Example 3: Different Units of Measurement

Question: A parallelogram has a base of 40 cm and a slanted side of 0.5 m. Find the perimeter of the parallelogram.

• Step 1: Convert to the same unit. Since 1 metre = 100 cm, the side length is 0.5 \times 100 = 50\text{ cm}.

• Step 2: Identify values. Side a = 40\text{ cm}, Side b = 50\text{ cm}.

• Step 3: Apply the formula. P = 2(a + b).

• Step 4: Calculate. P = 2(40 + 50) = 2(90).

• Result: P = 180\text{ cm}.

Example 4: Finding the Base from Perimeter

Question: If the perimeter of the parallelogram is 120 mm and the adjacent side is 25 mm, how to calculate the base?

• Step 1: Identify values. P = 120, Side b = 25.

• Step 2: Set up the equation. 120 = 2(a + 25).

• Step 3: Solve for 'a'. Divide 120 by 2, which gives 60 = a + 25.

• Step 4: Subtract. 60 - 25 = 35.

• Result: The base a = 35\text{ mm}.

Example 5: Ratio-Based Dimensions

Question: The sides of a parallelogram are in the ratio 3:2. If the longer side is 15 cm, find the perimeter of the parallelogram.

• Step 1: Find the shorter side. If 3 parts equal 15 cm, then 1 part is 5 cm (15 \div 3). Therefore, 2 parts (the shorter side) = 2 \times 5 = 10\text{ cm}.

• Step 2: Identify values. Side a = 15\text{ cm}, Side b = 10\text{ cm}.

• Step 3: Apply formula. P = 2(15 + 10).

• Step 4: Calculate. P = 2(25)$.

• Result: P = 50\text{ cm}.

Read More - Perimeter - Definition, Unit, Formula and Examples

Comparison: Perimeter vs Area

To prevent making mistakes on tests, it is important to know the difference between these two ideas:

 Finding the perimeter is a basic ability that helps you learn more complicated geometry. You can quickly and correctly solve these issues by remembering that you only need two side lengths and that the height is utilised for area, not perimeter.

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