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

Below is the parallelogram ABCD.

AEC = 90°

What is the area of the parallelogram?

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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