How to Calculate Area?
In order to calculate the area of a shape, we can utilize a grid as a helpful tool. The area of any given shape can be determined by counting the number of unit squares that fit within its boundaries. These unit squares consist of many smaller squares, each with sides that measure \(1\) unit by \(1\) unit. Therefore, they are referred to as "unit squares". The accompanying diagram provides a visual representation of this process.
Let's use this method to calculate the area of the shape shown within the grid.
The area of this shape can be determined by counting the number of unit squares that are shaded.
Therefore, the area of the shape is equal to \(9\) square units. Let's consider another example where the shape doesn't completely occupy a unit square. In this case, we can make an estimation to determine its value. For instance, if it occupies approximately \(\frac{1}{2}\) of a unit square, we can combine two halves to form an area of \(1\) square unit. The diagram below provides a visual representation of this concept.
In this example, the shape occupies \(4\) complete squares and \(8\) half squares, giving it a total area of \(8\) square units. When the shaded region is less than \(\frac{1}{2}\), we can simply omit those parts. In the case of regular shapes, we can use specific formulas to calculate their area accurately. It is important to keep in mind, however, that these methods provide only an approximation of the true value.
Area of a Rectangle
The area of a rectangle can be determined by the amount of space it occupies. For example, in the grid below, the yellow rectangle occupies \(6\) units.
In the previous example, the rectangle has a length of \(3\) units and a width of \(2\) units. We can calculate its area by multiplying these dimensions, which is equivalent to counting the number of unit squares it occupies. Therefore, the formula for the area of a rectangle is: \(Area = length \times width\). In this particular case, the area would be \(2 \times 3 = 6\) square units.
Area of a Square
The area of a square can be determined by the amount of space it occupies. For instance, in the grid below, the colored square occupies a total of \(25\) squares.
By examining the figure, we can see that each side of the colored square measures \(5\) units in length. As a result, we can calculate the square's area by using the formula: \(Area = side \times side\), where "side" represents the length of one of its sides. For this particular square, the area would be \(5 \times 5 = 25\) square units.
Area of a Circle
A circle is a curved geometric shape. Its area represents the amount of space enclosed within the circle's boundary. Before delving into the formula for calculating a circle's area, it is important to understand concepts such as \(\pi\) and radius.
To determine the area of a circle, we utilize the formula: \(\pi r^{2}\), where "\(\pi\)" is a mathematical constant with an approximate value of \(3.14\) or \(\frac{22}{7}\), and "\(r\)" is the circle's radius.
