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 JTET Paper I, the focus is strictly on **plane figures** (2D shapes), specifically calculating their perimeter (boundary length) and area (surface enclosed). This topic forms a consistent 3–5 question chunk in the mathematics section.

Mastery of mensuration requires two things: memorizing the standard formulas and knowing when to apply which formula based on the shape described. Questions often present real-life contexts—fencing a field, tiling a floor, finding the cost of painting a wall—so recognizing the underlying geometric shape from word problems is essential.

Students must be comfortable with squares, rectangles, triangles, circles, and basic composite figures (shapes made by combining or removing simpler shapes). Speed and accuracy in calculation, especially with fractions and decimals, will determine success here.

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

• **Units matter**: Always check if the question gives dimensions in different units; convert them to the same unit before calculating.

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

• **Path and border problems** involve finding the area of a pathway around or inside a rectangle. This is calculated as: Area of outer rectangle − Area of inner rectangle.

• **Cost-based problems** multiply area or perimeter by the rate per unit to get total cost (e.g., cost of fencing = perimeter × rate per metre).

• **Diagonal of a rectangle** can be found using Pythagoras theorem: d = √(l² + b²), where l is length and b is breadth.

• **For circles**, remember that π ≈ 22/7 or 3.14 unless the question specifies otherwise.

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Formulas / Key Facts

### Rectangle

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

### Square

• Perimeter = 4 × side = 4a
• Area = side² = a²
• Diagonal = a√2

### Triangle (General)