Calculate the Area of a Square with Side Length 13 Units

Area Calculations with Perfect Squares

Look at the square below:

131313

What is its area?

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Find the area of the square
00:03 Find the side length of the square according to the given data
00:07 Use the formula to calculate the area of a square (side squared)
00:11 Substitute appropriate values and solve to find the area
00:18 And this is the solution to the problem

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Look at the square below:

131313

What is its area?

2

Step-by-step solution

The area of the square is equal to the side of the square raised to the second power.

That is:

A=L2 A=L^2

Since the drawing gives us one side of the square, and in a square all sides are equal, we will solve the area of the square as follows:

A=132=169 A=13^2=169

3

Final Answer

169 169

Key Points to Remember

Essential concepts to master this topic
  • Formula: Area of a square equals side length squared
  • Technique: Calculate A=132=13×13=169 A = 13^2 = 13 \times 13 = 169
  • Check: Verify that 169=13 \sqrt{169} = 13 matches the given side length ✓

Common Mistakes

Avoid these frequent errors
  • Adding instead of multiplying the side length
    Don't calculate 13 + 13 = 26 for area! This gives perimeter, not area. A square's area needs the space inside, which requires multiplication. Always use A=side2 A = side^2 for area calculations.

Practice Quiz

Test your knowledge with interactive questions

Look at the square below:

111111

What is the area of the square?

FAQ

Everything you need to know about this question

Why do I square the side length instead of just doubling it?

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Area measures space inside the shape! When you have a 13×13 square, you're filling it with 13 rows of 13 unit squares each. That's 13 × 13 = 169 total unit squares.

What's the difference between area and perimeter of a square?

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Area = space inside = side2 side^2
Perimeter = distance around = 4×side 4 \times side
For this square: Area = 169, Perimeter = 52

How can I remember the area formula for squares?

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Think "side squared" - you're making a square number! The word "square" in math comes from this shape. A 13×13 square gives you 13² = 169.

What if I get a really big number like 169?

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That's normal for area! Area grows quickly because you're multiplying length × width. Always check: does 169=13 \sqrt{169} = 13 ? If yes, your answer is correct!

Can I use a calculator for 13²?

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Yes! But try to recognize perfect squares like 13² = 169. Knowing common perfect squares (1², 2², 3²... up to 15²) will make geometry much faster.

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