Calculate Parallelogram Perimeter: Finding Total Length of 15cm and 10cm Sides

Q: Why can't I just add 15 + 10 to get the perimeter?

Because a perimeter is the total distance around the entire shape! A parallelogram has four sides, not two. You need to account for all four sides: two sides of 15 cm and two sides of 10 cm.

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

Opposite sides are always equal in parallelograms. If you label the corners A, B, C, D going around, then AB = CD and BC = AD. Think of it like a rectangle that's been 'pushed' sideways!

Q: What if the problem only gives me one side length?

You need at least two different side lengths to find a parallelogram's perimeter. If you only have one measurement, the problem cannot be solved unless it's a special case like a rhombus (all sides equal).

Q: Is the formula P = 2(a + b) the same for rectangles?

Yes! A rectangle is actually a special type of parallelogram where all angles are 90°. The perimeter formula $ P = 2(a + b) $ works for both shapes.

Q: Can I use P = 2a + 2b instead of P = 2(a + b)?

Absolutely! Both formulas are mathematically equivalent. $ P = 2(a + b) = 2a + 2b $. Use whichever version feels more comfortable to you.

Parallelogram Perimeter with Adjacent Side Lengths

The parallelogram ABCD has two sides measuring 15 cm and 10 cm. What is its perimeter?

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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

00:04 The perimeter of the parallelogram equals the sum of its sides

00:09 Opposite sides are equal in a parallelogram, so we'll multiply each side

00:16 We'll substitute appropriate values according to the given data, and solve for the perimeter

00:24 And this is the solution to the problem

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

The parallelogram ABCD has two sides measuring 15 cm and 10 cm. What is its perimeter?

Step-by-step solution

To solve this problem, follow these steps:

Step 1: Understand the properties of a parallelogram.
Step 2: Apply the perimeter formula for a parallelogram.
Step 3: Compute the value using the given side lengths.

Now, let's calculate:

Step 1: In a parallelogram, opposite sides are of equal length. Here, $AB = CD = 15 \, \text{cm}$ and $BC = DA = 10 \, \text{cm}$ .

Step 2: The perimeter $P$ of a parallelogram is calculated using the formula:

$P = 2(a + b)$

where $a$ and $b$ are the lengths of two adjacent sides.

Step 3: Substituting the given values for $a$ and $b$ :

$P = 2(15 + 10) = 2 \times 25 = 50 \, \text{cm}$

Therefore, the perimeter of parallelogram ABCD is 50 cm.

Among the choices, option 1: 50 cm is the correct answer.

Final Answer

50 cm

Key Points to Remember

Essential concepts to master this topic

Property: Opposite sides in parallelograms are always equal in length
Formula: Use P = 2(a + b) where a and b are adjacent sides
Check: Count all four sides: 15 + 10 + 15 + 10 = 50 cm ✓

Common Mistakes

Avoid these frequent errors

Adding only the two given side lengths
Don't just add 15 + 10 = 25 cm! This ignores that parallelograms have four sides, not two. A perimeter measures the total distance around the entire shape. Always remember that opposite sides are equal, so multiply by 2: P = 2(15 + 10) = 50 cm.

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 15 + 10 to get the perimeter?

Because a perimeter is the total distance around the entire shape! A parallelogram has four sides, not two. You need to account for all four sides: two sides of 15 cm and two sides of 10 cm.

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

Opposite sides are always equal in parallelograms. If you label the corners A, B, C, D going around, then AB = CD and BC = AD. Think of it like a rectangle that's been 'pushed' sideways!

What if the problem only gives me one side length?

You need at least two different side lengths to find a parallelogram's perimeter. If you only have one measurement, the problem cannot be solved unless it's a special case like a rhombus (all sides equal).

Is the formula P = 2(a + b) the same for rectangles?

Yes! A rectangle is actually a special type of parallelogram where all angles are 90°. The perimeter formula $P = 2(a + b)$ works for both shapes.

Can I use P = 2a + 2b instead of P = 2(a + b)?

Absolutely! Both formulas are mathematically equivalent. $P = 2(a + b) = 2a + 2b$ . Use whichever version feels more comfortable to you.

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