Mensuration: Area and Perimeter of Simple Plane Figures

Overview

Mensuration is the branch of mathematics dealing with the measurement of geometric figures—their lengths, areas, and volumes. For Bihar TET 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 Bihar TET mathematics sections, typically carrying 2–4 questions. Questions range from direct formula application to word problems involving fencing, flooring, painting walls, or finding dimensions when area/perimeter is given. Mastery requires memorizing formulas and understanding when to apply each one.

Students must be comfortable with squares, rectangles, triangles, circles, and simple composite figures. The ability to visualize shapes and convert units (cm to m, m² to cm²) is equally essential for scoring full marks.

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Key Concepts

• **Perimeter** is the total length of the boundary of a closed figure. Think of it as the length of wire needed to fence a plot. Unit: metre (m), centimetre (cm).

• **Area** is the amount of surface enclosed by a figure. Think of it as the number of unit squares that fit inside the shape. Unit: square metre (m²), square centimetre (cm²).

• **Perimeter is a linear measure (one-dimensional); area is a square measure (two-dimensional).** This distinction matters when converting units.

• For **composite figures** (L-shaped rooms, pathways), break the shape into simpler figures, calculate separately, then add or subtract as needed.

• **Circumference** is the perimeter of a circle. The ratio of circumference to diameter is always π (pi), approximately 22/7 or 3.14.

• When a **path or border** surrounds a rectangle, the path area = Area of outer rectangle − Area of inner rectangle.

• **Unit conversion rule**: 1 m = 100 cm, so 1 m² = 10,000 cm². Always ensure consistent units before calculating.

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Formulas / Key Facts

### Square (side = a)

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

### Rectangle (length = l, breadth = b)

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

### Triangle

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