Rectangle Perimeter Calculation: Area = 18 Square Units

Q: Why is the perimeter 18 when the area is also 18?

This is just a coincidence for this specific rectangle! The area formula is $ length \times width $ while perimeter is $ 2 \times (length + width) $. They happen to equal the same number here.

Q: Do I need to use the area information given?

The area helps you verify your work! Once you find the side lengths from the diagram (6 and 3), check that $ 6 \times 3 = 18 $ matches the given area.

Q: What's the quickest way to find perimeter?

Use the formula: $ P = 2(l + w) $ where l = length and w = width. So $ P = 2(6 + 3) = 2(9) = 18 $.

Q: Can a rectangle's perimeter and area ever be equal?

Yes! It happens when the dimensions work out mathematically. Try different rectangles: a 4×4 square has perimeter 16 and area 16, while a 5×2.25 rectangle has both equal to 14.5.

Rectangle Perimeter with Given Area

If the area of the rectangle below is equal to 18.

Calculate the perimeter of the rectangle.

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Determine the perimeter of the rectangle

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

00:09 Opposite sides are equal in a rectangle

00:16 Substitute the relevant values into the formula according to the given data and proceed to solve for the perimeter

00:20 This is the solution

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

If the area of the rectangle below is equal to 18.

Calculate the perimeter of the rectangle.

Step-by-step solution

Given that in a rectangle every pair of opposite sides are equal to each other, we can state that:

$AB=CD=6$

$AC=BD=3$

To calculate the perimeter of the rectangle, we add all the sides together:

$3+6+3+6=6+12=18$

Final Answer

Key Points to Remember

Essential concepts to master this topic

Formula: Perimeter equals sum of all four rectangle sides
Technique: Add opposite sides twice: 3 + 6 + 3 + 6 = 18
Check: Verify area calculation: length × width = 6 × 3 = 18 ✓

Common Mistakes

Avoid these frequent errors

Calculating area instead of perimeter
Don't multiply length × width = 6 × 3 = 18 when asked for perimeter! This gives you the area which is already given. Always add all sides together: 3 + 6 + 3 + 6 = 18 for perimeter.

Practice Quiz

Test your knowledge with interactive questions

Look at the rectangle below.

Side DC has a length of 1.5 cm and side AD has a length of 9.5 cm.

What is the perimeter of the rectangle?

FAQ

Everything you need to know about this question

Why is the perimeter 18 when the area is also 18?

This is just a coincidence for this specific rectangle! The area formula is $length \times width$ while perimeter is $2 \times (length + width)$ . They happen to equal the same number here.

How do I know which sides are length and width?

It doesn't matter which you call length or width! In this rectangle, the sides are 6 and 3. Either way: $6 \times 3 = 18$ or $3 \times 6 = 18$ .

Do I need to use the area information given?

The area helps you verify your work! Once you find the side lengths from the diagram (6 and 3), check that $6 \times 3 = 18$ matches the given area.

What's the quickest way to find perimeter?

Use the formula: $P = 2(l + w)$ where l = length and w = width. So $P = 2(6 + 3) = 2(9) = 18$ .

Can a rectangle's perimeter and area ever be equal?

Yes! It happens when the dimensions work out mathematically. Try different rectangles: a 4×4 square has perimeter 16 and area 16, while a 5×2.25 rectangle has both equal to 14.5.

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