Calculate Side Length AD in a Parallelogram with Perimeter 24cm and AB = 8

Q: Why are opposite sides equal in a parallelogram?

By definition, a parallelogram has opposite sides that are parallel and equal. This means AB = CD and AD = BC, which is the key property that makes this problem solvable!

Q: Can I use the same method for any parallelogram perimeter problem?

Yes! The formula Perimeter = 2(side1) + 2(side2) works for any parallelogram. Just identify which sides are given and solve for the unknown.

Q: What if the diagram shows different side lengths?

Always trust the given information over what the diagram appears to show. Diagrams aren't always drawn to scale, but the numerical values are always accurate.

Q: How do I know which sides are opposite to each other?

In parallelogram ABCD, the sides that don't share a vertex are opposite. So AB is opposite to CD, and AD is opposite to BC.

Parallelogram Properties with Perimeter Calculations

A parallelogram has a perimeter of 24 cm.

AB = 8

How long is side AD?

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Find AD

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

00:06 Opposite sides are equal in a parallelogram, so multiply each side

00:10 Substitute appropriate values according to the given data, and solve for AD

00:20 Isolate AD

00:30 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

A parallelogram has a perimeter of 24 cm.

AB = 8

How long is side AD?

Step-by-step solution

Each pair of opposite sides are parallel and equal.

AB is parallel to DC and therefore also AB = DC = 8.

We will use the given perimeter to find AD and BC—which are also equal and parallel to each other.

Let's now calculate the perimeter of the parallelogram:

$24=2AB+2AD$

$24=16+2AD$

$24-16=2AD$

$8=2AD$

Then, we'll divide the two sides by 2:

$\frac{8}{2}=\frac{2AD}{2}$

$AD=4$

Final Answer

$4$

Key Points to Remember

Essential concepts to master this topic

Property: Opposite sides of parallelograms are equal in length
Formula: Perimeter = 2AB + 2AD = 2(8) + 2AD = 24
Check: Verify: 4 + 4 + 8 + 8 = 24 cm total perimeter ✓

Common Mistakes

Avoid these frequent errors

Adding all four sides as different values
Don't treat AB, BC, CD, and AD as four different unknown lengths = impossible to solve! This ignores the key parallelogram property. Always remember opposite sides are equal: AB = CD and AD = BC.

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 are opposite sides equal in a parallelogram?

By definition, a parallelogram has opposite sides that are parallel and equal. This means AB = CD and AD = BC, which is the key property that makes this problem solvable!

Can I use the same method for any parallelogram perimeter problem?

Yes! The formula Perimeter = 2(side1) + 2(side2) works for any parallelogram. Just identify which sides are given and solve for the unknown.

What if the diagram shows different side lengths?

Always trust the given information over what the diagram appears to show. Diagrams aren't always drawn to scale, but the numerical values are always accurate.

How do I know which sides are opposite to each other?

In parallelogram ABCD, the sides that don't share a vertex are opposite. So AB is opposite to CD, and AD is opposite to BC.

Could AD be longer than AB?

Absolutely! There's no rule that says one pair of sides must be longer than the other. In this case, AD (4 cm) is actually shorter than AB (8 cm).

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