Rectangle Perimeter Calculation: Finding Distance Around a 63-Square-Unit Shape

Rectangle Perimeter with Given Area

If the area of the rectangle below is 63.

Calculate the perimeter of the rectangle.

636363999777AAABBBDDDCCC

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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 Opposite sides are equal in a rectangle
00:08 Substitute the relevant values into the formula according to the given data
00:13 The perimeter of the rectangle equals the sum of its sides
00:19 Substitute the relevant values into the formula according to the given data and proceed to solve to determine the perimeter
00:44 This is the solution

Step-by-step written solution

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1

Understand the problem

If the area of the rectangle below is 63.

Calculate the perimeter of the rectangle.

636363999777AAABBBDDDCCC

2

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=9 AB=CD=9

AC=BD=7 AC=BD=7

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

7+9+7+9=14+18=32 7+9+7+9=14+18=32

3

Final Answer

32

Key Points to Remember

Essential concepts to master this topic
  • Rectangle Properties: Opposite sides are equal, length and width given
  • Technique: Add all four sides: 9 + 7 + 9 + 7 = 32
  • Check: Verify area: 9 × 7 = 63 square units ✓

Common Mistakes

Avoid these frequent errors
  • Using area formula for perimeter
    Don't use Area = length × width to find perimeter = wrong formula! Area measures space inside, perimeter measures distance around. Always use Perimeter = 2(length + width) or add all four sides.

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?
666444AAABBBCCCDDD

FAQ

Everything you need to know about this question

Why can't I just use the area to find perimeter directly?

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Area and perimeter measure different things! Area tells you the space inside (63 square units), while perimeter tells you the distance around the edges. You need the actual side lengths.

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

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Look at the diagram! The length is usually the longer side (9 units) and the width is the shorter side (7 units). But for perimeter, it doesn't matter which is which!

Do I need to add all four sides or can I use a formula?

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Both work! You can add all four sides: 9+7+9+7=32 9 + 7 + 9 + 7 = 32 OR use the formula: P=2(l+w)=2(9+7)=32 P = 2(l + w) = 2(9 + 7) = 32

What if the rectangle was rotated differently?

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The perimeter stays the same! Whether the rectangle is horizontal, vertical, or tilted, the side lengths don't change, so the perimeter remains 32 units.

How can I double-check my perimeter answer?

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Verify the area matches: 9×7=63 9 \times 7 = 63 ✓ Then ensure your perimeter uses the correct sides. Also check that opposite sides are equal in your calculation.

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