Mensuration: Area and Perimeter of Plane Figures

Overview

Mensuration is the branch of mathematics dealing with measurement of geometric figures—their lengths, areas, and volumes. For Assam TET Paper I, the focus is on **plane figures** (2D shapes), specifically calculating their perimeter (boundary length) and area (surface covered).

This topic carries significant weight in the mathematics section and appears consistently in TET examinations. Questions typically involve direct formula application, word problems related to real-life situations (fencing a field, tiling a floor, painting a wall), and composite figures combining two or more shapes. Mastery requires memorizing formulas and understanding when to apply each.

Students must be comfortable with basic arithmetic operations, unit conversions, and visualizing shapes. The pedagogy component may also ask how to teach mensuration concepts to primary students using concrete materials like tiles, paper cutouts, and grid sheets.

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 critical—all measurements must be in the same unit before calculation. Convert cm to m or vice versa as needed.

• **Composite figures** are shapes formed by combining simple figures. Find the area by adding areas of component shapes or subtracting the removed portion.

• **Relationship between perimeter and area**: Two figures can have the same perimeter but different areas, and vice versa. They are independent measures.

• **Square and rectangle** are the most frequently tested shapes, followed by triangle, parallelogram, and circle.

• For **circles**, understand the difference between radius (centre to boundary) and diameter (diameter = 2 × radius).

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

• Perimeter = sum of all three sides = a + b + c
• Area (general) = ½ × base × height
• Area (Heron's formula): When three sides a, b, c are given and s = (a + b + c)/2, then Area = √[s(s−a)(s−b)(s−c)]