Rectangle Perimeter Calculation: Area = 24, Find the Distance Around

Q: Why don't I need to use the area of 24?

The area is extra information in this problem! Since you can already see the length is 6 and width is 4 on the diagram, you have everything needed for perimeter. The area just confirms that $ 6 \times 4 = 24 $.

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

In rectangles, opposite sides are always equal. So the top and bottom sides have the same length, and the left and right sides have the same length.

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

Area measures the space inside (length × width). Perimeter measures the distance around the outside (add all four sides). They're completely different measurements!

Q: Can I use the formula P = 2l + 2w?

Absolutely! $ P = 2(6) + 2(4) = 12 + 8 = 20 $. This formula works because rectangles have two pairs of equal opposite sides.

Q: What if the rectangle had different dimensions?

The same method applies! Just identify the length and width from the diagram, then either add all four sides or use $ P = 2l + 2w $.

Rectangle Perimeter with Given Dimensions

The area of the rectangle below is equal to 24.

Calculate the perimeter of the rectangle.

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Understand the problem

The area of the rectangle below is equal to 24.

Calculate the perimeter of the rectangle.

Step-by-step solution

Given that in a rectangle all pairs of opposite sides are equal to each other, it can be argued that:

$AB=CD=6$

$AC=BD=4$

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

$4+4+6+6=$

$8+12=20$

In other words, the data of the rectangle's area is unnecessary, since we already have all the data to calculate the perimeter, and we do not need to calculate the other sides.

Final Answer

Key Points to Remember

Essential concepts to master this topic

Formula: Perimeter equals sum of all four sides
Technique: Add opposite sides: $6 + 6 + 4 + 4 = 20$
Check: Verify opposite sides are equal: length = 6, width = 4 ✓

Common Mistakes

Avoid these frequent errors

Using area to find perimeter instead of given side lengths
Don't calculate perimeter using area = 24 when dimensions are already shown! Area tells you length × width, but you already see length = 6 and width = 4 on the diagram. Always use the given side measurements directly 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

Why don't I need to use the area of 24?

The area is extra information in this problem! Since you can already see the length is 6 and width is 4 on the diagram, you have everything needed for perimeter. The area just confirms that $6 \times 4 = 24$ .

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

In rectangles, opposite sides are always equal. So the top and bottom sides have the same length, and the left and right sides have the same length.

What's the difference between area and perimeter?

Area measures the space inside (length × width). Perimeter measures the distance around the outside (add all four sides). They're completely different measurements!

Can I use the formula P = 2l + 2w?

Absolutely! $P = 2(6) + 2(4) = 12 + 8 = 20$ . This formula works because rectangles have two pairs of equal opposite sides.

What if the rectangle had different dimensions?

The same method applies! Just identify the length and width from the diagram, then either add all four sides or use $P = 2l + 2w$ .

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