If the perimeter of a square floor is 32 m, find its area.
We are given a square floor with a perimeter of \(32 \text{ m}\). The perimeter of a square is the sum of its four equal sides, which can be expressed by the formula:
\[P = 4s\]
where \(P\) is the perimeter and \(s\) is the length of one side. Knowing the perimeter is \(32 \text{ m}\), we can find the side length by dividing the perimeter by 4.
Given the perimeter formula \(P = 4s\), we substitute \(P = 32 \text{ m}\):
\[32 \text{ m} = 4s\]
Dividing both sides by 4 gives:
\[s = \frac{32 \text{ m}}{4} = 8 \text{ m}\]
The length of each side of the square floor is \(8 \text{ m}\).
The area \(A\) of a square is calculated using the formula:
\[A = s^2\]
Substituting the side length \(s = 8 \text{ m}\) into the formula:
\[A = (8 \text{ m})^2 = 8 \text{ m} \times 8 \text{ m} = 64 \text{ m}^2\]
Therefore, the area of the square floor is \(64 \text{ m}^2\). This matches option 'a'.
When renovating a room, if you know the total length of the baseboards needed for a square room (the perimeter), you can use this method to calculate the total floor area. Knowing the area is essential for buying the right amount of flooring material, such as tiles or carpet. For example, if your square room has a total perimeter of \(32 \text{ m}\), calculating the area ensures you purchase exactly \(64 \text{ m}^2\) of flooring, minimizing waste and costs.