Calculate Rectangle Side Length: Given Area 42 cm² and Height 12 cm

Rectangle Area Calculations with Known Dimensions

Below is the rectangle ABCD.

It has an area of 42 cm² and side AD is equal to 12 cm.

What is the length of side DC?
S=42S=42S=42121212AAABBBCCCDDD

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Determine the value of side DC
00:03 Apply the formula for calculating the area of a rectangle (side x side)
00:09 Substitute in the relevant values according to the given data and proceed to solve for DC
00:12 Isolate DC
00:16 This is the solution

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Below is the rectangle ABCD.

It has an area of 42 cm² and side AD is equal to 12 cm.

What is the length of side DC?
S=42S=42S=42121212AAABBBCCCDDD

2

Step-by-step solution

Remember that to calculate the area of the rectangle, we multiply the length by the width.

Therefore:

42=12×CD 42=12\times CD

42=12CD 42=12CD

Divide both sides by 12:

3.5=CD 3.5=CD

3

Final Answer

3.5

Key Points to Remember

Essential concepts to master this topic
  • Area Formula: Rectangle area equals length times width
  • Technique: Use A=l×w A = l \times w to find missing side: 42 = 12 × DC
  • Check: Multiply result by known side: 3.5 × 12 = 42 cm² ✓

Common Mistakes

Avoid these frequent errors
  • Adding dimensions instead of multiplying
    Don't calculate 42 = 12 + DC which gives DC = 30! Addition gives perimeter components, not area. Always use multiplication for area: A = length × width.

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 we divide 42 by 12 instead of subtracting?

+

Because area uses multiplication! The formula A = length × width means 42 = 12 × DC. To solve for DC, we need the opposite operation of multiplication, which is division.

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

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It doesn't matter! In rectangles, you can call either dimension length or width. The area formula works the same way: Area = side₁ × side₂.

What if my answer seems too small?

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Check your work! If one side is large (like 12 cm) and the area is not huge (42 cm²), then the other side should be smaller. That's mathematically correct!

Can I use this method for any rectangle problem?

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Yes! As long as you know the area and one side length, you can always find the missing side by dividing: Missing side=AreaKnown side \text{Missing side} = \frac{\text{Area}}{\text{Known side}}

How do I check if 3.5 cm is reasonable?

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Multiply it back: 3.5 × 12 = 42 cm². Since this matches the given area, 3.5 cm is correct! Always verify by checking that length × width = given area.

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