16.3 Area and perimeter of squares
Perimeter is the total distance around the outside of a shape.
Area is the total space or surface of a flat shape.
- perimeter
- the total distance around the outside of a shape
- area
- the total space or surface of a flat shape
In the diagram below, the green line shows the perimeter of the square and the pink surface shows the area of the square.
The perimeter of a square is equal to the sum of the lengths of its four sides. We know that all sides of a square are equal in length, so the perimeter is equal to four times the length of the square (\(s\)).
The area of a square is equal to the length of a side squared:
\[\text{Area of a square } = s \times s = s^2\]Worked example 16.6: Calculating the perimeter of a square
Determine the perimeter of the square.
Calculate the perimeter of the square.
To determine the perimeter, we must find the sum of all four sides:
\[\text{Perimeter of the square } = 7 + 7 + 7 + 7 = 4 \times 7 = 28 \text{ m}\]Write the final answer.
\[\text{Perimeter of the square} = 28 \text{ m}\]Hint: Always remember to include the units in the answer.
Worked example 16.7: Calculating the area of a square
Find the area of the square.
