A square has sides of length 10 yards. What is the area?
The correct answer and explanation is:
The area of a square can be calculated using the formula: Area=side length2\text{Area} = \text{side length}^2
In this case, the side length of the square is given as 10 yards. To find the area, simply square the side length: Area=102=100 square yards\text{Area} = 10^2 = 100 \, \text{square yards}
Thus, the area of the square is 100 square yards.
The concept of area is crucial in understanding how much space a two-dimensional shape occupies. The square, being a special type of rectangle where all sides are equal, allows for a straightforward calculation of area. Each side of the square contributes to the total area, and since all sides are equal in length, squaring one side length gives the total area.
In general, for any shape with uniform dimensions, area is calculated by multiplying the length and width of the shape. For a square, since the length and width are the same, this multiplication becomes squaring the side length. This formula simplifies the process for calculating area when dealing with squares.
To visualize this, imagine a 10-yard by 10-yard grid. If you were to fill each of the smaller 1-yard by 1-yard squares within this larger square, you would have a total of 100 smaller squares, each representing 1 square yard. This helps confirm that the area of the square is indeed 100 square yards.
In real-world applications, knowing how to calculate the area of a square is useful for determining how much material is needed to cover a surface, like flooring or fabric for a square-shaped piece. It is a fundamental concept in geometry and is used in a wide range of fields including architecture, engineering, and construction.