Calculate Areas of Three Squares: 3x3, 6x6, and 4x4 Units in Notation Form

Square Areas with Exponential Notation

In the figure in front of you there are 3 squares

Write down the area of the shape in potential notation

333666444

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Write down the area of the shape in powers notation
00:03 We'll write the formula for the entire shape's area
00:06 In squares all sides
00:09 We'll use the formula for calculating square area (side times side)
00:13 We'll do this for each square and sum up the areas
00:26 A power is writing a number multiplied by itself several times:
00:30 Therefore we'll convert multiplication to power
00:34 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

In the figure in front of you there are 3 squares

Write down the area of the shape in potential notation

333666444

2

Step-by-step solution

Using the formula for the area of a square whose side is b:

S=b2 S=b^2 In the picture, we are presented with three squares whose sides from left to right have a length of 6, 3, and 4 respectively:

Therefore the areas are:

S1=32,S2=62,S3=42 S_1=3^2,\hspace{4pt}S_2=6^2,\hspace{4pt}S_3=4^2 square units respectively,

Consequently the total area of the shape, composed of the three squares, is as follows:

Stotal=S1+S2+S3=32+62+42 S_{\text{total}}=S_1+S_2+S_3=3^2+6^2+4^2 square units

To conclude, we recognise through the rules of substitution and addition that the correct answer is answer C.

3

Final Answer

62+42+32 6^2+4^2+3^2

Key Points to Remember

Essential concepts to master this topic
  • Formula: Area of square with side b is b2 b^2 square units
  • Technique: Express each area as an exponent: 32+62+42 3^2 + 6^2 + 4^2
  • Check: Verify dimensions match figure: 3×3, 6×6, and 4×4 squares ✓

Common Mistakes

Avoid these frequent errors
  • Writing multiplication instead of exponents
    Don't write 3×3 + 6×6 + 4×4 = incorrect notation! This shows the calculation but not the proper mathematical form. Always use exponential notation 32+62+42 3^2 + 6^2 + 4^2 when asked for 'potential notation'.

Practice Quiz

Test your knowledge with interactive questions

\( 112^0=\text{?} \)

FAQ

Everything you need to know about this question

What does 'potential notation' mean in this context?

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Potential notation here means using exponents to show how area is calculated. Instead of writing 3×3, we write 32 3^2 to show the side length is raised to the power of 2.

Why do we use exponents for square areas?

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Because area of a square equals side × side, which is the same as side squared. Writing 62 6^2 is more elegant than 6×6 and shows the mathematical relationship clearly.

Do I need to calculate the final numerical answer?

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No! The question asks for the area in notation form, so 32+62+42 3^2 + 6^2 + 4^2 is the complete answer. Don't calculate 9 + 36 + 16 = 61.

What if the squares were in a different order?

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The order doesn't matter for addition! Whether you write 32+62+42 3^2 + 6^2 + 4^2 or 62+42+32 6^2 + 4^2 + 3^2 , both are correct because addition is commutative.

How do I identify which number goes with which square?

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Look carefully at the figure labels. Each square has its side length marked. The smallest square is 3×3, the largest is 6×6, and the medium one is 4×4.

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