Perimeter of a square is 48 cm. Find its area.
Understand the Problem
The question is asking us to find the area of a square given its perimeter. To solve this, we first need to calculate the side length of the square using the perimeter formula, and then we can use that side length to find the area.
Answer
$$ A = \left( \frac{P}{4} \right)^2 $$
Answer for screen readers
The area of the square is given by the formula: $$ A = \left( \frac{P}{4} \right)^2 $$
Steps to Solve
- Understanding the perimeter formula for a square
The perimeter $P$ of a square can be found using the formula: $$ P = 4s $$ where $s$ represents the length of one side of the square.
- Solving for the side length
To find the side length $s$, we can rearrange the formula for perimeter: $$ s = \frac{P}{4} $$
- Finding the area of the square
Once we have the side length $s$, we can calculate the area $A$ using the formula: $$ A = s^2 $$
- Substituting the side length into the area formula
Finally, after calculating the side length, substitute $s$ into the area formula to find the area of the square: $$ A = \left( \frac{P}{4} \right)^2 $$
The area of the square is given by the formula: $$ A = \left( \frac{P}{4} \right)^2 $$
More Information
This method shows how we utilize the relationship between perimeter and area in geometric figures. Knowing the perimeter simplistically leads us to calculate the area through basic algebraic manipulations.
Tips
- Failing to remember that the perimeter of a square is four times the side length, leading to incorrect calculations for the side.
- Forgetting to square the side length when calculating the area.
AI-generated content may contain errors. Please verify critical information
