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 which 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.
| 1. | What Is the Meaning of Area? |
| 2. | How to Calculate Area? |
| 3. | Area of Geometric Shapes |
| 4. | Solved Examples on Area |
| 5. | Practice Questions on Area |
| 6. | FAQs on Area |
What Is the Meaning of Area?
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.
How to Calculate Area?
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. Let's assume that each side of the unit square is 1 unit.
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 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.
Area of Geometric Shapes - Formula
Each shape has different dimensions and formulas.The following table shows the list of formulas for the area of various shapes.
| Shape | Area of Shapes - Formula |
|---|---|
|
Square
|
Area of a square = x2 square units |
|
Rectangle
|
Area of a rectangle = length × width = l × w square units
|
|
Circle |
Area of a circle = π r2 square units |
|
Triangle
|
Area of a triangle =\(\dfrac{1}{2}\times b \times h\) square units
|
|
Parallelogram |
Area of a parallelogram = base × height = b × h square units
|
|
Isosceles Trapezoid
|
Area of an isosceles trapezoid = \(\dfrac{1}{2}(a+b) h\) square units
|
|
Rhombus
|
Area of a rhombus = \(\dfrac{1}{2}\times (d1) \times (d2)\) square units
|
|
Kite
|
Area of a kite = \(\dfrac{1}{2}\times (d1) \times (d2)\)square units
|
Related Topics on Area
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.
Solved Examples on Area
-
Example 1: Find the area of a square with side 7 cm.
Solution:
Area of a square = side × side. Here, side = 7 cm
Substituting the values, 7 × 7= 49.
Therefore, the area of the square = 49 square cm.
-
Example 2: The dimensions of a rectangle are 15 cm and 8 cm. Find its area.
Solution:
The area of a rectangle is the product of its length and width, which can be represented by the formula: Area = l × w.
Substituting the given values, we get area of the rectangle = 15 × 8 = 120 cm2 -
Example 3: Can you find the area of a circle with a radius of 14 cm?
Solution:
Radius of the circle = 14 cm
Area of a circle is calculated by the formula π r2
Substituting the values in the formula, area = \(\dfrac{22}{ 7}\) × 14 × 14 = 616 square cm.
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Example 4: Calculate the area of the given shape by counting the squares.
Solution: Let's calculate the full squares and the half squares.
There are 24 unit squares and 5 half squares.
Therefore, the area of the shape = 24 + (5 × ½ ) = 24 + 2.5 26.5 square units
Frequently Asked Questions(FAQs)
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: 1/2 × 2 × π × r × r. Therefore, the area of the circle is π r2.
What is Perimeter?
The total length of the boundary of a closed shape is called its perimeter. In other words, perimeter is the sum of the sides of a 2-dimensional shape.
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. 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.