Calculate Parallelogram Perimeter: Using Side Lengths 7 and 10

Q: Why can't I just add 10 + 7 = 17 for the perimeter?

Perimeter means the total distance around the shape! You need all four sides: two sides of length 10 and two sides of length 7. So it's 10 + 10 + 7 + 7 = 34.

Q: How do I know which sides are equal in a parallelogram?

Opposite sides are always equal in parallelograms. If you label vertices A, B, C, D going around, then AB = CD and BC = AD. Look for sides that are across from each other.

Q: What if the parallelogram looks tilted or slanted?

The shape doesn't matter for perimeter! Whether it's a rectangle, rhombus, or slanted parallelogram, you still add up all four sides the same way.

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

Add the sides in a different order: 7 + 10 + 7 + 10 = 34. Or use the formula: $ 2 \times 7 + 2 \times 10 = 14 + 20 = 34 $. Same answer means you're correct!

Parallelogram Perimeter with Given Side Lengths

Calculate the perimeter of the given parallelogram.

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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 Opposite sides are equal in a parallelogram

00:08 Let's substitute the side value

00:15 These sides are also opposite therefore equal

00:21 Let's substitute the side value

00:32 The perimeter of the parallelogram equals the sum of its sides

00:50 Let's substitute appropriate values and solve for the perimeter

00:59 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 given parallelogram.

Step-by-step solution

As is true for a parallelogram each pair of opposite sides are equal and parallel,

Therefore it is possible to argue that:

$AC=BD=7$

$AB=CD=10$

Now we can calculate the perimeter of the parallelogram by adding together all of its sides:

$10+10+7+7=20+14=34$

Final Answer

Key Points to Remember

Essential concepts to master this topic

Property: Opposite sides of a parallelogram are equal in length
Technique: Add all four sides: 10 + 7 + 10 + 7
Check: Verify opposite sides match: AB = CD = 10, AC = BD = 7 ✓

Common Mistakes

Avoid these frequent errors

Adding only two adjacent sides and doubling
Don't calculate 2(10 + 7) = 34 without understanding why! This shortcut only works because opposite sides are equal in parallelograms. Always identify which sides are equal first, then apply the formula P = 2(a + b).

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 can't I just add 10 + 7 = 17 for the perimeter?

Perimeter means the total distance around the shape! You need all four sides: two sides of length 10 and two sides of length 7. So it's 10 + 10 + 7 + 7 = 34.

How do I know which sides are equal in a parallelogram?

Opposite sides are always equal in parallelograms. If you label vertices A, B, C, D going around, then AB = CD and BC = AD. Look for sides that are across from each other.

Can I use the formula P = 2(a + b)?

Yes! This is a great shortcut. Since opposite sides are equal, you only need two different side lengths: $P = 2(10 + 7) = 2(17) = 34$ .

What if the parallelogram looks tilted or slanted?

The shape doesn't matter for perimeter! Whether it's a rectangle, rhombus, or slanted parallelogram, you still add up all four sides the same way.

How can I double-check my perimeter calculation?

Add the sides in a different order: 7 + 10 + 7 + 10 = 34. Or use the formula: $2 \times 7 + 2 \times 10 = 14 + 20 = 34$ . Same answer means you're correct!

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