Mensuration: Area and Perimeter of Simple Plane Figures
Overview
Mensuration is the branch of mathematics dealing with measurement of geometric figures—their lengths, areas, and volumes. For OTET Paper I, the focus is strictly on **plane figures** (2D shapes), specifically calculating their perimeter (boundary length) and area (surface covered).
This topic appears consistently in OTET mathematics sections, typically carrying 2–4 questions. Questions range from direct formula application to word problems involving fields, gardens, paths, and picture frames. Mastery requires memorizing formulas and understanding when to apply each—particularly in composite figure problems where shapes combine or one is cut from another.
Students must be comfortable with unit conversions (cm to m, m² to cm²) and able to visualize real-world applications like fencing a plot (perimeter) or tiling a floor (area).
---
Key Concepts
- **Perimeter** is the total length of the boundary of a closed figure. Think of it as the length of wire needed to form the shape's outline.
- **Area** is the amount of surface enclosed within 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); area is measured in square units (cm², m², km²). Converting 1 m = 100 cm means 1 m² = 10,000 cm².
- **Composite figures** are formed by combining or removing simple shapes. Calculate by adding or subtracting individual areas/perimeters appropriately.
- **Path problems** involve a path around or inside a rectangle/square. The path area equals outer area minus inner area.
- For **circles**, π (pi) is taken as 22/7 or 3.14 unless specified otherwise in the question.
- **Semi-circle perimeter** includes both the curved part (half circumference) and the diameter.
- In word problems, identify the shape first, extract dimensions, then apply the correct formula.
---
Formulas / Key Facts
### Rectangle (length = l, breadth = b)
- Perimeter = 2(l + b)
- Area = l × b
- Diagonal = √(l² + b²)
### Square (side = a)
- Perimeter = 4a
- Area = a²
- Diagonal = a√2
### Triangle (sides a, b, c; base = b, height = h)
- Perimeter = a + b + c