Rectangle-Square Area Ratio: Find Area When Square = 16 cm²

Area Ratios with Square Side Calculations

The rectangle ABCD is divided into the rectangle KBCM and the square AKMD.

The ratio between the rectangle and the square is 2:1.

The area of square AKMD is 16 cm².

Calculate the area of rectangle KBCM.

AAABBBCCCDDDKKKMMMS=18

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:18 Let's calculate the area of rectangle K, B, C, M. Ready?
00:24 The ratio of the areas is given. Let's use this data step by step.
00:32 Now, substitute the given values in place. Let's solve for the area!
00:44 To get rid of fractions, multiply every part by 18. You're doing great!
00:50 And that's how we find the solution. Well done!

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

The rectangle ABCD is divided into the rectangle KBCM and the square AKMD.

The ratio between the rectangle and the square is 2:1.

The area of square AKMD is 16 cm².

Calculate the area of rectangle KBCM.

AAABBBCCCDDDKKKMMMS=18

2

Step-by-step solution

First we will divide the area of KBCM by the area of AKMD.

We know that their ratio is 2:1, therefore:

KBCMAKMD=21 \frac{KBCM}{AKMD}=\frac{2}{1}

We also know the area of AKMD, so we'll substitute it into the formula to obtain the following:

KBCM18=21 \frac{KBCM}{18}=\frac{2}{1}

Finally, we multiply by 18:

KBCM=2×18=36 KBCM=2\times18=36

3

Final Answer

32

Key Points to Remember

Essential concepts to master this topic
  • Ratio Relationship: Rectangle to square area ratio 2:1 means rectangle area = 2 × square area
  • Square Area Formula: If area = 16 cm², then side length = √16 = 4 cm
  • Check Method: Verify that rectangle area ÷ square area = 2 ÷ 1 = 2 ✓

Common Mistakes

Avoid these frequent errors
  • Using the wrong given area value
    Don't use area = 18 from the diagram when the problem states 16 cm² = wrong calculation! The diagram may show different values for illustration. Always use the area value given in the problem text.

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 does the diagram show S=18 but the problem says 16 cm²?

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Diagrams are often illustrative examples that may show different values than the actual problem. Always use the numbers given in the problem text, not the diagram!

How do I use a 2:1 ratio to find the rectangle area?

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A 2:1 ratio means the rectangle area is 2 times the square area. So if the square area is 16 cm², the rectangle area = 2 × 16 = 32 cm².

Do I need to find the side length of the square?

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Not for this problem! You can work directly with areas. The ratio tells you: rectangle area = 2 × square area = 2 × 16 = 32 cm²

What if I calculated the rectangle area as 48 cm²?

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You might have misread the ratio or used wrong values. Check: ratio 2:1 means rectangle = 2 × 16 = 32, not 3 × 16 = 48.

How can I verify my answer is correct?

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Check the ratio: 3216=21 \frac{32}{16} = \frac{2}{1} ✓ The rectangle area divided by square area should equal 2.

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