Area is the amount of space covered by a two-dimensional shape. It represents the total surface enclosed by the boundary of a closed figure and is measured in square units.
Area of a rectangle
The concept of area helps us understand how much surface a shape occupies and allows us to compare the sizes of different shapes.
Example: John wants to paint a wall. The length of the wall is 15 feet, and its width is 8 feet. The area of the wall tells us how much paint is required to cover it.
Area of the wall = length × width = 120 square feet (ft²).
Area using complete unit squares
Unit squares
Area of the shape = 9 square units.
The area of a shape is the amount of surface it covers. When a shape is drawn on a grid, we can find its area by counting unit squares.
• Each small square in the grid has sides 1 unit × 1 unit. • So, the area of one small square is 1 square unit. • Such a square is called a unit square.
Area When the Shape Covers Half Squares
Partially covers shape
Area of the shape = 8 square units.
Sometimes, a shape does not completely cover the unit squares. In such cases, we estimate the area.
• A square covered halfway is counted as 1/2 square unit. • Two half squares make one full square. • Very small parts (less than half) are usually ignored.
Area of Simple Shapes
In geometry, the area of shapes like quadrilaterals, a circle that means 2d shapes can be found using simple formulas.
Area of complex shapes can be found by breaking them into smaller simple shapes like triangles, squares, and rectangles. A complex shape is formed by joining many straight line segments. After finding the area of each simple shape, we add them to get the total area.
For example, the area of the following shape can be found by breaking it down into a rectangle and a triangle:
Solution: The complex figure is broken into a rectangle and a triangle as shown in the figure,
