Calculate Rectangle Area: Given Perimeter 30cm and Height 5cm

Rectangle Area with Given Perimeter

Look at the rectangle in the figure.

P=30P=30P=30555

Its perimeter is 30 cm.

What is its area?

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:05 Let's find the area of rectangle A, B, C, D.
00:10 The perimeter is found by adding up all the sides of the rectangle.
00:17 Remember, in a rectangle, opposite sides are equal.
00:24 Plug in the values you have into the formula to find the lengths of the sides.
00:29 We've arranged the equation to have all unknowns on one side.
00:37 This gives us the lengths of sides A, B and D, C.
00:42 Now, let's use the formula to calculate the rectangle's area.
00:48 Insert the known values and solve to find the area. And that's it!

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Look at the rectangle in the figure.

P=30P=30P=30555

Its perimeter is 30 cm.

What is its area?

2

Step-by-step solution

The perimeter of the rectangle equals the sum of all its sides, which means:

P=AB+BC+CD+DA P=AB+BC+CD+DA

Since in a rectangle each pair of opposite sides are equal, we can say that:

BC=AD=5 BC=AD=5

This means that the two sides together equal 10, and now we'll subtract them from the perimeter and get:

AB+DC=3010=20 AB+DC=30-10=20

This means sides AB and DC together equal 20, and since they are equal to each other, we'll divide 20 to find out how much each one equals:

20:2=10 20:2=10

Now we'll multiply side AB by side BC to find the area of the rectangle:

10×5=50 10\times5=50

3

Final Answer

50 cm²

Key Points to Remember

Essential concepts to master this topic
  • Formula: Perimeter = 2 × length + 2 × width
  • Technique: From P = 30 and height = 5, find 2 × width = 20
  • Check: Area = 10 × 5 = 50, verify P = 2(10) + 2(5) = 30 ✓

Common Mistakes

Avoid these frequent errors
  • Confusing perimeter formula with area formula
    Don't use P = length × width to find missing side = wrong dimension! This confuses area and perimeter formulas completely. Always remember perimeter is the sum of all four sides: P = 2l + 2w.

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 divide the perimeter by 4 to find each side?

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Because rectangles don't have all equal sides like squares do! You know one side (height = 5), so you need to use P=2l+2w P = 2l + 2w to find the other.

How do I know which side is length and which is width?

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It doesn't matter for area calculation! Whether you call the unknown side length or width, Area = side₁ × side₂ gives the same result.

What if I get confused between perimeter and area formulas?

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Remember: Perimeter is around the shape (add all sides), Area is inside the shape (multiply length × width). Very different purposes!

Can I solve this without using algebra?

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Yes! Since you know height = 5, and there are two heights in the perimeter, that's 10 cm total. The remaining 20 cm must be the two lengths, so each length = 10 cm.

How do I check if my area answer is reasonable?

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Compare to familiar objects! 50 cm² is about the size of your hand or a small book. Does that seem right for a 10×5 rectangle? Trust your intuition!

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