Mensuration — Area and Perimeter of Plane Figures

Overview

Mensuration is the branch of mathematics that deals with measurement of geometric figures — their lengths, areas and volumes. For JKTET Paper I, the focus is on **plane figures** (2D shapes), specifically calculating their **perimeter** (boundary length) and **area** (surface covered). This topic forms a reliable scoring area in the mathematics section, with 2–4 questions typically appearing.

Students must master the standard formulas for common shapes and develop the ability to apply them in word problems involving real-life contexts — fencing a field, tiling a floor, finding the cost of painting a wall. The pedagogy component also expects you to understand how children learn measurement concepts through concrete experiences before moving to abstract formulas.

The key to success is not just memorising formulas but understanding what perimeter and area actually represent, recognising which formula applies to which shape, and handling unit conversions confidently.

Key Concepts

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

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

• **Unit consistency** is essential — all measurements must be in the same unit before applying any formula.

• **Composite figures** are shapes made by combining two or more basic shapes. Find the area by adding or subtracting the areas of component shapes.

• **Relationship between perimeter and area** — two figures can have the same perimeter but different areas, and vice versa. A square has the maximum area for a given perimeter among rectangles.

• **For circles**, the perimeter is called **circumference**. The constant π (pi) ≈ 22/7 or 3.14 connects the diameter to the circumference.

• **Semi-circle perimeter** includes the curved part plus the diameter (the straight edge).

Formulas / Key Facts

### Rectangle

• Perimeter = 2 × (length + breadth) = 2(l + b)
• Area = length × breadth = l × b
• Diagonal = √(l² + b²)

### Square

• Perimeter = 4 × side = 4a
• Area = side × side = a²
• Diagonal = a × √2

### Triangle (General)

• Perimeter = sum of all three sides = a + b + c
• Area = ½ × base × height = ½ × b × h