Calculate Rectangle Area: Given BC=5 and Perimeter=40

Rectangle Area with Given Perimeter

ABCD is a rectangle.

BC = 5

Perimeter = 40

Calculate the area of the rectangle.

555AAABBBCCCDDD

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Calculate the area of rectangle ABCD
00:03 The perimeter of the rectangle equals the sum of its sides
00:15 The area of the rectangle equals side(AB) multiplied by side (BC)
00:32 We'll substitute appropriate values in the perimeter formula and solve for the side
00:41 Opposite sides are equal in a rectangle
00:54 We'll arrange the equation and solve for AB
01:07 We'll isolate AB
01:14 This is the length of side AB
01:20 Now we can use the formula to calculate the rectangle's area
01:26 We'll substitute appropriate values and solve for the area
01:31 This is the solution

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

ABCD is a rectangle.

BC = 5

Perimeter = 40

Calculate the area of the rectangle.

555AAABBBCCCDDD

2

Step-by-step solution

The perimeter of the rectangle equals:

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

Since we know that BC equals 5 and in a rectangle opposite sides are equal to each other, we get:

40=AB+5+CD+5 40=AB+5+CD+5

40=10+AB+CD 40=10+AB+CD

Since AB equals CD we can write the equation as follows:

40=2AB+10 40=2AB+10

Let's move 10 to the other side and change the sign accordingly:

4010=2AB 40-10=2AB

30=2AB 30=2AB

Let's divide both sides by 2:

15=AB 15=AB

Now we know the length and width of the rectangle and can calculate its area:

15×5=75 15\times5=75

3

Final Answer

75

Key Points to Remember

Essential concepts to master this topic
  • Rectangle Property: Opposite sides are equal in length
  • Technique: Use P=2l+2w P = 2l + 2w to find unknown side: 40 = 2(15) + 2(5)
  • Check: Verify area calculation: 15 × 5 = 75 square units ✓

Common Mistakes

Avoid these frequent errors
  • Adding all sides instead of using perimeter formula
    Don't just write BC + BC + AB + AB = 5 + 5 + AB + AB without recognizing the rectangle property! This makes the problem unnecessarily complicated and prone to errors. Always use the formula P = 2l + 2w to find unknown dimensions efficiently.

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 do opposite sides have the same length in a rectangle?

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By definition, a rectangle is a quadrilateral with four right angles. This geometric property automatically makes opposite sides parallel and equal in length!

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

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Absolutely! Both P=2l+2w P = 2l + 2w and P=2(l+w) P = 2(l + w) are correct. Use whichever feels more comfortable - they give the same result.

What if BC was the length instead of the width?

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It doesn't matter! In rectangles, you can call either pair of sides 'length' and 'width'. The area formula A=l×w A = l \times w works regardless of which dimension you call length or width.

How do I know which side is 5 from looking at the diagram?

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Look for the labeled measurement in the diagram. The side BC is marked with '5', so BC = 5. The diagram shows BC is one of the shorter sides of this rectangle.

Why do we multiply the two sides to get area?

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Area measures how many unit squares fit inside the rectangle. When you have 15 units along one side and 5 units along the other, you get 15 × 5 = 75 unit squares total!

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