Perimeter and Area

Overview

Perimeter and Area form the backbone of mensuration at the primary level and appear consistently in WB TET Paper I Mathematics. These concepts test a candidate's ability to apply formulas to plane figures and solve word problems involving fencing, flooring, painting and similar real-life contexts.

For WB TET, you must master the basic formulas for square, rectangle and triangle, understand the distinction between perimeter (boundary length) and area (surface covered), and convert between units when required. Questions often combine these concepts with cost calculations — for example, finding the cost of fencing a rectangular plot or tiling a square room.

Conceptual clarity matters more than rote memorisation. Examiners frequently test whether candidates can identify which formula applies to a given situation and whether they can handle composite figures or missing-dimension problems.

---

Key Concepts

• **Perimeter** is the total length of the boundary of a closed plane figure. It is measured in linear units (cm, m, km).

• **Area** is the amount of surface enclosed within the boundary. It is measured in square units (cm², m², km²).

• For any figure, perimeter and area are independent properties — two figures can have the same perimeter but different areas, and vice versa.

• **Square**: All four sides equal; all angles 90°. Perimeter depends on one measurement (side), area depends on side squared.

• **Rectangle**: Opposite sides equal; all angles 90°. Perimeter uses length and breadth; area is their product.

• **Triangle**: Three-sided polygon. Perimeter is the sum of all three sides; area requires base and corresponding height.

• **Unit consistency** is crucial. Always ensure all measurements are in the same unit before applying formulas.

• **Composite figures** can be broken into simpler shapes. Find individual areas/perimeters and combine appropriately.

---

Formulas / Key Facts

### Square (side = a) | Property | Formula | |----------|---------| | Perimeter | P = 4a | | Area | A = a² | | Diagonal | d = a√2 |

### Rectangle (length = l, breadth = b) | Property | Formula | |----------|---------| | Perimeter | P = 2(l + b) | | Area | A = l × b | | Diagonal | d = √(l² + b²) |

### Triangle (sides a, b, c; base = b; height = h) | Property | Formula | |----------|---------| | Perimeter | P = a + b + c | | Area (using base and height) | A = ½ × base × height | | Area (Heron's formula) | A = √[s(s−a)(s−b)(s−c)], where s = (a+b+c)/2 |