Calculate Parallelogram Perimeter: 12-Unit Base with 7-Unit Side Length

Q: Why are opposite sides equal in a parallelogram?

In a parallelogram, opposite sides are parallel and never meet. This geometric property forces them to be equal in length. It's like having two pairs of parallel lines!

Q: How do I know which sides are opposite?

Opposite sides are the ones that don't share a vertex. In parallelogram ABCD: AB is opposite to CD, and BC is opposite to AD. They're like the top-bottom and left-right pairs.

Q: Can I use the formula P = 2(length + width)?

Yes! Since opposite sides are equal, you can use $ P = 2(a + b) $ where a and b are the lengths of adjacent sides: $ P = 2(12 + 7) = 2(19) = 38 $

Q: What if the parallelogram looks tilted or slanted?

The shape doesn't matter! Whether it's a rectangle, rhombus, or slanted parallelogram, the rule stays the same: opposite sides are equal. Always use the given side lengths, not how it looks.

Q: How can I double-check my perimeter calculation?

Add the sides in a different order: $ 7 + 12 + 7 + 12 = 38 $ or use the formula $ P = 2(7 + 12) = 38 $. Both methods should give the same answer!

Parallelogram Perimeter with Opposite Sides

Calculate the perimeter of the parallelogram ABCD, given that CD is parallel to AB.

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Calculate the perimeter of the parallelogram

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

00:07 Opposite sides are equal in a parallelogram

00:18 Let's substitute appropriate values according to the given data, and solve for the perimeter

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

Calculate the perimeter of the parallelogram ABCD, given that CD is parallel to AB.

Step-by-step solution

First we need to remember that pairs of opposite sides in a parallelogram are parallel and equal.

Therefore, AB is parallel to CD and BC is parallel to AD.

From this we can conclude that AB = CD = 7.

Also: BC = AD = 12.

Finally we can calculate the perimeter by adding all the sides together:

$7+7+12+12=14+24=38$

Final Answer

Key Points to Remember

Essential concepts to master this topic

Property: Opposite sides in parallelograms are equal and parallel
Technique: Add all four sides: AB + BC + CD + AD
Check: Verify opposite sides match: AB = CD = 12, BC = AD = 7 ✓

Common Mistakes

Avoid these frequent errors

Using only two sides to calculate perimeter
Don't just add 12 + 7 = 19! This gives only two sides, not the full perimeter. The perimeter needs all four sides around the shape. Always add opposite pairs: 12 + 7 + 12 + 7 = 38.

Practice Quiz

Test your knowledge with interactive questions

Find the perimeter of the parallelogram using the data below.

FAQ

Everything you need to know about this question

Why are opposite sides equal in a parallelogram?

In a parallelogram, opposite sides are parallel and never meet. This geometric property forces them to be equal in length. It's like having two pairs of parallel lines!

How do I know which sides are opposite?

Opposite sides are the ones that don't share a vertex. In parallelogram ABCD: AB is opposite to CD, and BC is opposite to AD. They're like the top-bottom and left-right pairs.

Can I use the formula P = 2(length + width)?

Yes! Since opposite sides are equal, you can use $P = 2(a + b)$ where a and b are the lengths of adjacent sides: $P = 2(12 + 7) = 2(19) = 38$

What if the parallelogram looks tilted or slanted?

The shape doesn't matter! Whether it's a rectangle, rhombus, or slanted parallelogram, the rule stays the same: opposite sides are equal. Always use the given side lengths, not how it looks.

How can I double-check my perimeter calculation?

Add the sides in a different order: $7 + 12 + 7 + 12 = 38$ or use the formula $P = 2(7 + 12) = 38$ . Both methods should give the same answer!

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