Mensuration
Mensuration
Mensuration is the branch of mathematics that deals with measurement of geometric shapes and figures. It helps us calculate different quantities such as perimeter, area, surface area, and volume. These measurements are very useful in everyday life.
For example, when building a house, laying tiles on a floor, fencing a field, or designing a container, we use the concepts of mensuration.
Types of Mensuration
Mensuration can be divided into two main categories:
- 2D Mensuration (Plane Figures)
- 3D Mensuration (Solid Figures)
2D Shapes
Two-dimensional shapes have only length and breadth. They lie on a flat surface.
Examples include:
- Square
- Rectangle
- Triangle
- Circle
- Parallelogram
For these shapes, we usually calculate perimeter and area.
Perimeter
The perimeter of a shape is the total length of its boundary. To find the perimeter, we add the lengths of all sides.
Example
A rectangle has length = 8 cm and breadth = 5 cm.
Perimeter = 2 × (length + breadth)
Perimeter = 2 × (8 + 5)
Perimeter = 2 × 13
Perimeter = 26 cm
Perimeter of Common Shapes
- Square = 4 × side
- Rectangle = 2 × (length + breadth)
- Triangle = Sum of all sides
Area
The area of a shape represents the space inside the boundary of the shape. Area is measured in square units such as cm², m², or km².
Area of Rectangle
Area = length × breadth
Length = 10 cm
Breadth = 6 cm
Area = 10 × 6 = 60 cm²
Area of Square
Area = side × side = side²
Side = 7 cm
Area = 7 × 7 = 49 cm²
Area of Triangle
Area = ½ × base × height
Base = 8 cm
Height = 6 cm
Area = ½ × 8 × 6 = 24 cm²
Area of Parallelogram
Area = base × height
Base = 9 cm
Height = 5 cm
Area = 45 cm²
3D Shapes
Three-dimensional shapes have length, breadth, and height. They occupy space and therefore have volume.
Examples include:
- Cube
- Cuboid
- Cylinder
- Cone
- Sphere
For these shapes, we calculate surface area and volume.
Surface Area
Surface area is the total area of all the surfaces of a solid object.
Surface area of cube = 6 × side²
Surface area of cuboid = 2(lb + bh + hl)
These formulas help calculate how much material is required to cover a box or paint a wall.
Volume
Volume measures the amount of space inside a solid object.
Volume of cube = side³
Volume of cuboid = length × breadth × height
Example
Length = 5 cm
Breadth = 4 cm
Height = 3 cm
Volume = 5 × 4 × 3 = 60 cm³
Units in Mensuration
- Perimeter → cm, m, km
- Area → cm², m²
- Volume → cm³, m³
Applications of Mensuration
Mensuration is widely used in everyday life:
- Construction and architecture
- Agriculture and land measurement
- Designing rooms and furniture
- Packaging and storage
- Engineering and manufacturing
By learning mensuration, students develop the ability to solve real-world problems involving measurement and space.