What is the definition of “area”?
Area is defined as the amount of space taken up by a shape or a region. All flat or two-dimensional surfaces have an area. A wall, a tabletop, and the cover of a notebook have surface areas. We often use the quantity known as area for real-life activities like painting walls, carpeting floors, laying tiles in swimming pools, and so on.
How do we measure the area of a shape?
The area of a shape can be measured by counting the number of squares that can fit inside the boundary of the shape. While using squares to measure the area of a shape, we need to make sure that the squares being used here are of the same area. Let’s consider the following shape as an example.
The area of this shape can be determined by placing small squares (of the same area) inside it.
By counting the number of squares in this shape, we get the area of the entire shape as the area equivalent to that of 30 small squares. Since we don’t know the area of these squares yet, we can’t find the actual area of the shape.
Note that the small squares are of a standard size in the previous case. If the small squares are of different sizes, it would make things complicated.
Even though the shape is divided into smaller squares in this case, these squares are not of the same size. So, it makes it difficult to express the area of the shaded region without using a standard unit.
Measuring area using standard units
The most basic unit of area is a square unit. A square unit is defined as a square having sides of unit length. The area of a shape can be measured by counting the number of square units that would fit inside the boundary of the shape.
Each side is 1 unit long.
The area of this square is 1 square unit.
The standard units of area include square centimeters, square inches, square feet, square meters, and so on
The unit of area is applied to a situation according to the size of the region being measured.
Each side is 1 inch long.
The area of this square is 1 square inch.
Unit for Measuring Area Examples
Example 1: Find the area of the rectangle shaded in blue.
Solution: The blue rectangle is made up of 28 squares that have a unit area.
Hence, Area = 28 square units
Example 2: Find the area of the shaded region.
Solution: The shaded region is made up of 22 squares, each having an area of 1 square inch.
Hence, Area = 22 square inches
Example 3: The layout of the ground floor of a shopping mall is given below. The white cells represent the corridor of the shopping mall and the coloured cells represent the area covered by different outlets.
- a. Determine which part of the shopping mall takes up most of the area.
- b. Determine which shop has the smallest area, and find its area.
- c. Find the area covered by shop F.
Solution: First, let’s count the number of unit squares covered by each shop in the shopping mall.
a. It is evident that the corridor takes up most of the available space.
Area covered by the corridor = 38 square meters.
b. Shop E, which looks like a kiosk, takes up the least area when compared to the rest of the outlets.
Area of shop E = 2 square meters
c. Area of shop F = 15 square meters
Example 4: Is the area of a king-size quilt more likely to be 45 square feet or 45 square meters?
Solution: Quilts are used to cover beds. A king-size bed can be covered using a king-size quilt. The dimensions of a king-size bed are usually 6.3 feet x 6.6 feet, giving us an area of about 41 square feet. On the other hand, 45 square meters is the area of a small swimming pool.
Hence, the area of a king-size quilt is around 45 square feet and not 45 square meters.
All two-dimensional shapes have areas. Additionally, all three-dimensional solids have surface areas.
Only closed two-dimensional shapes have an area. Area cannot be calculated for any open two-dimensional shapes.
Area is often used for multiple purposes in the fields of construction, agriculture, and many fields of science and engineering.