Area

Area is the amount of space occupied by a two-dimensional figure. In other words, it is the quantity that measures the number of unit squares that cover the surface of a closed figure. The standard unit of area is square units which is generally represented as square inches, square feet, etc. Let's learn how to calculate the area of different geometric shapes through examples and practice questions.

The word 'area' means a vacant surface. The area of a shape is calculated with the help of its length and width. Length is unidimensional and measured in units such as feet (ft), yards (yd), inches (in), etc. However, the area of a shape is a two-dimensional quantity. Hence, it is measured in square units like square inches or (in²), square feet or (ft ²), square yard or (yd²), etc. Most of the objects or shapes have edges and corners. The length and width of these edges are considered while calculating the area of a specific shape.

Let us see how to calculate the area of a shape with the help of a grid. The area of any shape is the number of unit squares that can fit into it. The grid is made up of many squares of sides 1 unit by 1 unit. The area of each of these squares is 1 square unit. Hence, each square is known as a unit square. Look at the figure shown below. Let us find the area of the shape drawn in the grid.

The area of this shape is the number of shaded unit squares.

Thus, the area of the shape = 9 square units. Now, let us look at another example. When the shape does not occupy a complete unit square, we can approximate and find its value. If it occupies about 1/2 of the unit square, we can combine two such halves to form an area of 1 square unit. Observe the figure given below.

Here, the area occupied by the shape = 4 full squares and 8 half squares. Together this forms an area of 8 square units. If the shaded region is less than 1/2, we can omit those parts. For regular shapes, we have certain formulas to calculate their area. Note that this is only an approximate value.

Area of a Rectangle

The area of a rectangle is the space occupied by it. Consider the yellow rectangle in the grid. It has occupied 6 units.

In the above example, the length of the rectangle is 3 units and the width is 2 units. The area of a rectangle is obtained by multiplying its length and width which is the same as counting the unit squares. Thus, the formula for the area of a rectangle is: Area of the rectangle = length × width. In this case, it will be 2 × 3 = 6 square units.

Area of a Square

The area of a square is the space occupied it. Look at the colored square shown in the grid below. It occupies 25 squares.

From the figure, we can observe that the length of each side of the colored square is 5 units. Therefore, the area of the square is the product of its sides which can be represented by the formula: Area of a square = side × side. So, the area of this square = 5 × 5 = 25 square units.

Area of a Circle

A circle is a curved shape. The area of a circle is the amount of space enclosed within the boundary of a circle. Learn more about π and radius before we go to the formula for the area of a circle.

The area of a circle is calculated with the help of the formula: π r², where π is a mathematical constant whose value is approximated to 3.14 or 22/7 and r is the radius of the circle.

Each shape has different dimensions and formulas. The following table shows the list of formulas for the area of various shapes.

☛ Related Topics on Area

Check out the following topics related to areas of different shapes and learn more about area formulas.

• Geometric Area Formula
• Area of Triangle

Tips and Tricks

• We often memorize the formulas for calculating the area of shapes. An easier method would be to use grid lines to understand how the formula has been derived.
• We often get confused between the area and perimeter of a shape. A thorough understanding can be built by tracing the surface of any shape and observing that the area is essentially the space or the region covered by the shape.

What is an Area?

The area of a shape is a two-dimensional quantity that is measured in square units like square inches or (in²), square feet or (ft²), square yard or (yd²), etc.

How do You Find the Area of Irregular Shapes?

The area of irregular shapes can be found by dividing the shape into unit squares. When the shape does not occupy the complete unit square, we can approximate and find its value.

How do You Prove the Area of the Circle?

If a circle is folded into a triangle, the radius becomes the height of the triangle and the perimeter becomes its base which is 2 × π × r. We know that the area of the triangle is found by multiplying its base and height and then dividing by 2, which is: ½ × 2 × π × r × r. Therefore, the area of the circle is π r².

What is Perimeter and Area of Triangle?

The total length of the boundary of a closed shape is called its perimeter. In other words, the perimeter is the sum of the sides of a 2-dimensional shape. The perimeter of the triangle is the sum of three sides of the triangle whereas the area of the triangle is

What are the Formulas for Area and Perimeter of a Square and Rectangle?

The formulas for the area and perimeter of a square and a rectangle are as follows. Area of a square = side × side. The perimeter of a square = 4 × side. Area of a rectangle = length × breadth. Perimeter of a rectangle = 2 ×(length + width)

Why is Area Expressed in Square Units?

The area of a shape is the number of unit squares required to completely cover it. Therefore, it is measured and expressed in square units.