Mensuration — Area and Perimeter of Plane Figures

Overview

Mensuration is the branch of mathematics dealing with the measurement of geometric figures — their lengths, areas and volumes. For CG TET Paper I, the focus is strictly on **plane figures** (two-dimensional shapes), specifically calculating their **perimeter** (the total boundary length) and **area** (the space enclosed within the boundary).

This topic carries direct weightage in the mathematics section and also appears in pedagogy questions where you must explain how to teach these concepts to primary students. Questions typically involve rectangles, squares, triangles and circles — the shapes children encounter in Classes 3–5. Mastery requires memorising key formulas and knowing when to apply each one in word problems involving real-life contexts like fencing a field, tiling a floor or painting a wall.

The key skill tested is not just formula recall but the ability to identify which formula fits a given situation, convert units correctly and solve multi-step problems involving combined figures.

Key Concepts

• **Perimeter** is the total length of the boundary of a closed figure. Think of it as the length of wire needed to go around the shape exactly once.

• **Area** is the measure of the surface enclosed by a figure. Think of it as the number of unit squares needed to cover the shape completely.

• **Units matter**: Perimeter is measured in linear units (cm, m, km) while area is measured in square units (cm², m², km²). Converting between units is a common exam trap.

• **Rectangle vs Square**: A square is a special rectangle where all four sides are equal. This means square formulas are simplified versions of rectangle formulas.

• **Triangle types**: The basic formula (½ × base × height) works for all triangles, but the height must be perpendicular to the chosen base.

• **Circle terminology**: Radius (r) is the distance from centre to boundary; diameter (d) = 2r; π (pi) ≈ 22/7 or 3.14 for calculations.

• **Composite figures**: Many exam problems involve shapes made by combining or removing standard figures — solve by adding or subtracting individual areas.

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