Parallelogram Side Length: Finding Missing Side Given 12cm Perimeter

Q: Why does a parallelogram only have two different side lengths?

In parallelograms, opposite sides are always equal! So if AB = 4 cm, then CD = 4 cm too. Similarly, BC equals AD. This property makes calculating much easier.

Q: What if I don't know which sides are opposite?

Look at the parallelogram shape! Sides that don't touch each other are opposite. In parallelogram ABCD: AB is opposite to CD, and BC is opposite to AD.

Q: Can I use the same formula for rectangles and squares?

Yes! Rectangles and squares are special types of parallelograms, so $ P = 2a + 2b $ works for all of them. For squares, both sides are equal!

Q: What if my answer doesn't seem right?

Always check! Add up all four sides: $ 4 + 2 + 4 + 2 = 12 \text{ cm} $. If this equals the given perimeter, your answer is correct!

Perimeter with Opposite Sides

The parallelogram below has a perimeter of 12 cm.

AB = 4 cm

Calculate the length of the other side.

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Calculate the second side

00:03 The perimeter of the parallelogram equals the sum of the sides

00:13 Opposite sides are equal in a parallelogram

00:42 Collect like terms

00:49 Substitute appropriate values according to the given data, and solve for AC

01:00 Isolate AC

01:11 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

The parallelogram below has a perimeter of 12 cm.

AB = 4 cm

Calculate the length of the other side.

Step-by-step solution

To solve this problem, follow these steps:

Step 1: Identify the given information: one side $AB = 4 \, \text{cm}$ , and the perimeter $P = 12 \, \text{cm}$ .
Step 2: Apply the perimeter formula for parallelograms, $P = 2a + 2b$ .
Step 3: Solve for the other side $b$ .

Now, let's work through the calculations:

The formula for the perimeter of a parallelogram is:
$P = 2a + 2b$
Given $a = 4 \, \text{cm}$ and $P = 12 \, \text{cm}$ , substituting these values gives:
$12 = 2(4) + 2b$
Simplifying, we have:
$12 = 8 + 2b$
Subtract 8 from both sides:
$4 = 2b$
Divide both sides by 2 to find $b$ :
$b = 2$

Therefore, the length of the other side is $2 \, \text{cm}$ .

Final Answer

Key Points to Remember

Essential concepts to master this topic

Rule: In parallelograms, opposite sides are equal in length
Technique: Use $P = 2a + 2b$ where $a = 4$ and $P = 12$
Check: Verify: $2(4) + 2(2) = 8 + 4 = 12 \text{ cm}$ ✓

Common Mistakes

Avoid these frequent errors

Using perimeter formula for rectangles only
Don't think you need four different sides = overcomplicated solution! This ignores the key property of parallelograms. Always remember that opposite sides are equal, so you only need to find two different side lengths.

Practice Quiz

Test your knowledge with interactive questions

Given the parallelogram:

Calculate the perimeter of the parallelogram.

FAQ

Everything you need to know about this question

Why does a parallelogram only have two different side lengths?

In parallelograms, opposite sides are always equal! So if AB = 4 cm, then CD = 4 cm too. Similarly, BC equals AD. This property makes calculating much easier.

What if I don't know which sides are opposite?

Look at the parallelogram shape! Sides that don't touch each other are opposite. In parallelogram ABCD: AB is opposite to CD, and BC is opposite to AD.

Can I use the same formula for rectangles and squares?

Yes! Rectangles and squares are special types of parallelograms, so $P = 2a + 2b$ works for all of them. For squares, both sides are equal!

How do I solve for the unknown side step by step?

Follow this process: 1) Write the perimeter formula 2) Substitute known values 3) Solve the equation 4) Check your answer by calculating the total perimeter.

What if my answer doesn't seem right?

Always check! Add up all four sides: $4 + 2 + 4 + 2 = 12 \text{ cm}$ . If this equals the given perimeter, your answer is correct!

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