Area is the measure of the space covered by a two-dimensional shape. It is expressed in square units, such as square inches or square meters. For example, when we talk about the area of a rectangle, we mean the space covered by the rectangle on a flat surface.
Area is an important concept in geometry and is used to find the size of surfaces in real-life applications, such as calculating the area of a room for flooring or determining the amount of paint needed to cover a wall.
To find the area of a rectangle, multiply the length by the width. The formula for calculating the area of a rectangle is:
Area = Length * Width
Example: If a rectangle has a length of 6 units and a width of 4 units, the area would be:
Area = 6 * 4 = 24 square units
To find the area of a triangle, multiply the base by the height and then divide the result by 2. The formula is:
Area = (Base * Height) / 2
Example: If a triangle has a base of 8 units and a height of 5 units, the area would be:
Area = (8 * 5) / 2 = 20 square units
In three-dimensional figures with rectangular and triangular faces, the surface area is the sum of the areas of all the faces. To find the surface area, calculate the area of each face and add them together.
Example: Cube with sides of length 3 units:
Surface Area = 6 * (side * side) = 6 * (3 * 3) = 54 square units
The volume of a right rectangular prism is the measure of the space it encloses. Multiply the area of the base by the height:
Volume (V) = (Area of Base) * Height
Example: Base area 10 square units, height 5 units:
Volume = 10 * 5 = 50 cubic units
Problem: Find the area of a rectangle with a length of 9 units and a width of 5 units.
Solution:
Area = Length * Width Area = 9 * 5 = 45 square units
Problem: Calculate the volume of a right rectangular prism with a base area of 12 square units and a height of 8 units.
Solution:
Volume (V) = (Area of Base) * Height Volume = 12 * 8 = 96 cubic units