Find the Square Perimeter Function: Side Length 'a' Expression

Q: Why is the perimeter 4a and not just a?

A square has four equal sides, each with length a. To find the perimeter, you need to add all four sides together: $ a + a + a + a = 4a $.

Q: What's the difference between perimeter and area formulas?

Perimeter measures the distance around the square: $ P = 4a $Area measures the space inside the square: $ A = a^2 $Don't mix them up!

Q: Can I write the answer as P(a) = 4a instead of y = 4a?

Absolutely! Both $ P(a) = 4a $ and $ y = 4a $ represent the same function. The letter P makes it clearer that we're talking about perimeter.

Q: How do I remember this isn't 3a?

Think about it visually: a square has 4 sides, not 3! A triangle would have 3 sides, but squares always have exactly 4 equal sides to add up.

Square Perimeter with Variable Side Length

A square has a side length of a.

Choose the function that expresses the perimeter of the square.

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Express the perimeter of the square

00:03 In a square all sides are equal

00:08 The perimeter of the square equals the sum of its sides

00:13 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

A square has a side length of a.

Choose the function that expresses the perimeter of the square.

Step-by-step solution

To find the perimeter of the square with side length $a$ , we use the standard formula for the perimeter of a square:

$P = 4 \times (\text{side length}) = 4a$

This straightforward multiplication tells us that the perimeter is four times the side length because a square has four equal sides.

Therefore, the function that expresses the perimeter of the square is:

$y = 4a$

Among the given choices, the correct expression corresponding to this calculation is: $y = 4a$ .

Thus, the solution to this problem is $y = 4a$ .

Final Answer

$y=4a$

Key Points to Remember

Essential concepts to master this topic

Formula: Square perimeter equals four times the side length
Technique: For side length a, perimeter = 4a
Check: Count all four equal sides: a + a + a + a = 4a ✓

Common Mistakes

Avoid these frequent errors

Using area formula instead of perimeter
Don't use P = a² which gives you area! This squares the side length instead of adding all sides. Always remember perimeter = 4a for squares, not a².

Practice Quiz

Test your knowledge with interactive questions

Complete:

The missing value of the function point:

$$ f(x)=x^2 $$

$$ f(?)=16 $$

FAQ

Everything you need to know about this question

Why is the perimeter 4a and not just a?

A square has four equal sides, each with length a. To find the perimeter, you need to add all four sides together: $a + a + a + a = 4a$ .

What's the difference between perimeter and area formulas?

Perimeter measures the distance around the square: $P = 4a$
Area measures the space inside the square: $A = a^2$
Don't mix them up!

Can I write the answer as P(a) = 4a instead of y = 4a?

Absolutely! Both $P(a) = 4a$ and $y = 4a$ represent the same function. The letter P makes it clearer that we're talking about perimeter.

What if the side length was a number like 5 instead of 'a'?

Then you'd substitute the number: if side length = 5, then perimeter = $4 \times 5 = 20$ . The variable 'a' just represents any possible side length.

How do I remember this isn't 3a?

Think about it visually: a square has 4 sides, not 3! A triangle would have 3 sides, but squares always have exactly 4 equal sides to add up.

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