Question

What is the area of a square that has a perimeter of 12 feet?

Answer 1

Hint: We need to calculate the length of one side of the square using the formula $P=4a$ where P is the perimeter and a is the length of one side. We then need to calculate the area of a square which is given by the formula $A=a^2$ where A is the area of the square and a is the side length. The units for the area will be square feet or $f{t}^2.$

Complete step by step answer:
In order to solve this question, we first need to calculate the area of a square. A square is represented as shown in the figure below. It is a four-sided figure with all sides being equal in length. Let us assume the length of each side of the square is a. The perimeter is nothing but the total length of the sides of the square. Therefore, perimeter is 4a.

Given the perimeter is 12 feet,
$\Rightarrow P=4a$
Here, P represents perimeter and a represents the length of one side. Substituting the value of the perimeter here,
$\Rightarrow 12=4a$
Dividing both sides by 4,
$\Rightarrow {\displaystyle \frac{12}{4}}={\displaystyle \frac{4}{4}}a$
We divide the terms on the left-hand side of the equation,
$\Rightarrow 3=a$
Hence, the length of one side of the square is 3 feet. Now in order to find the area, we need to use the formula $A=a^2.$
Substituting the value of a here,
$\Rightarrow A=3^2$
We know that $3^2$ can be represented as $3\times 3,$
$\Rightarrow A=3\times 3=9$
Hence, the area of the square having a perimeter of 12 feet is 9 square feet or $9f{t}^2.$

Note: It is important to know the area and perimeter of standard figures. We also need to note that since for an area, we are multiplying the side length of two sides, its units also get multiplied twice. Therefore, we get the units of area as square feet which is same as $f{t}^2.$