What is Mensuration?
Mensuration is the branch of mathematics that deals with the measurement of geometric figures — their lengths, areas, and volumes. It helps us quantify the space occupied by 2D shapes and 3D solids.
Key Definitions:
- Perimeter: The total distance around the boundary of a 2D shape
- Area: The amount of surface enclosed within a 2D shape (square units)
Formulas for Common 2D Shapes:
| Shape | Perimeter | Area |
|---|---|---|
| **Rectangle** (length = l, breadth = b) | \(2(l + b)\) | \(l \times b\) |
| **Triangle** (base = b, height = h) | \(a + b + c\) | \(\frac{1}{2} \times b \times h\) |
| **Triangle** (using Heron's formula) | \(a + b + c\) | \(\sqrt{s(s-a)(s-b)(s-c)}\) where \(s = \frac{a+b+c}{2}\) |
| **Circle** (radius = r) | \(2\pi r\) (circumference) | \(\pi r^2\) |
Heron's Formula Details:
For a triangle with sides a, b, c:
- Semi-perimeter: \(s = \frac{a + b + c}{2}\)
- Area = \(\sqrt{s(s-a)(s-b)(s-c)}\)