Rectangle with Area 8: Calculate the Complete Perimeter

Q: What's the difference between area and perimeter?

Area is the space inside the rectangle (length × width). Perimeter is the distance around the outside (add all four sides). They measure completely different things!

Q: Why do I need to add all four sides if opposite sides are equal?

You're right that opposite sides are equal! So you can use $ 2 \times (length + width) $ or add each side individually: $ 4 + 2 + 4 + 2 = 12 $. Both methods give the same answer.

Q: How do I know which numbers are the length and width?

Look at the diagram carefully! The horizontal sides are labeled 4, and the vertical sides are labeled 2. These are your length and width dimensions.

Q: Can I use the area to find missing dimensions?

Yes! If you know the area and one dimension, use $ \text{other dimension} = \frac{\text{area}}{\text{known dimension}} $. Here: $ \frac{8}{4} = 2 $ confirms our width.

Q: Why is my answer 8 instead of 12?

You probably calculated the area instead of perimeter! $ 4 \times 2 = 8 $ is the area. For perimeter, add the sides: $ 4 + 2 + 4 + 2 = 12 $.

Rectangle Perimeter with Known Area

The area of a rectangle is equal to 8.

Calculate the perimeter of the rectangle.

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Understand the problem

The area of a rectangle is equal to 8.

Calculate the perimeter of the rectangle.

Step-by-step solution

According to the properties of the rectangle, all pairs of opposite sides are equal.

$AB=CD=8$

$AC=BD=2$

Now we calculate the perimeter of the rectangle by adding all the sides:

$4+4+2+2=8+4=12$

Final Answer

Key Points to Remember

Essential concepts to master this topic

Formula: Perimeter equals sum of all four sides
Technique: Use dimensions from diagram: 4 + 2 + 4 + 2
Check: Area calculation: length × width = 4 × 2 = 8 ✓

Common Mistakes

Avoid these frequent errors

Using area formula instead of perimeter formula
Don't calculate 4 × 2 = 8 thinking that's the perimeter! Area and perimeter are completely different measurements. Always add all four sides: 4 + 2 + 4 + 2 = 12 for perimeter.

Practice Quiz

Test your knowledge with interactive questions

Look at the rectangle ABCD below.

Side AB is 6 cm long and side BC is 4 cm long.

What is the area of the rectangle?

FAQ

Everything you need to know about this question

What's the difference between area and perimeter?

Area is the space inside the rectangle (length × width). Perimeter is the distance around the outside (add all four sides). They measure completely different things!

Why do I need to add all four sides if opposite sides are equal?

You're right that opposite sides are equal! So you can use $2 \times (length + width)$ or add each side individually: $4 + 2 + 4 + 2 = 12$ . Both methods give the same answer.

How do I know which numbers are the length and width?

Look at the diagram carefully! The horizontal sides are labeled 4, and the vertical sides are labeled 2. These are your length and width dimensions.

Can I use the area to find missing dimensions?

Yes! If you know the area and one dimension, use $\text{other dimension} = \frac{\text{area}}{\text{known dimension}}$ . Here: $\frac{8}{4} = 2$ confirms our width.

Why is my answer 8 instead of 12?

You probably calculated the area instead of perimeter! $4 \times 2 = 8$ is the area. For perimeter, add the sides: $4 + 2 + 4 + 2 = 12$ .

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