Class 9 · Chapter 6

Measuring Space: Perimeter and Area

Heron's formula, areas of quadrilaterals, and mixed shapes.

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Ganita Manjari · Class 9 (2026-27)

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Detailed theory

Compute semi-perimeter

s

. Then

A=\sqrt{s(s-a)(s-b)(s-c)}

. Powerful because no height needed.

Key concepts & formulas

**Heron's formula**:

A = \sqrt{s(s-a)(s-b)(s-c)}

where

s = (a+b+c)/2

Works for any triangle with known side lengths.

Area of parallelogram

= base\times height

Trapezium:

A = \tfrac 12(a+b)h

Composite shapes: decompose and add.