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

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

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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