14.7 Summary

Name: CBSE Class 8 Mathematics
Author: Vijayakumar P

Key Points

Area is counted in unit squares; perimeter is not a measure of area (shapes can share a perimeter yet differ in area, and the other way round).
Area of a rectangle = \text{length} \times \text{width}; a square of side s has area s^2.
Area of a triangle = \tfrac12 \times \text{base} \times \text{height}, true for every triangle. A median splits a triangle into two equal areas; triangles on the same base between two parallel lines all have equal area. With only the three sides, Heron’s formula gives the area.
The area of any polygon is found by cutting it into triangles and adding.
Area of a parallelogram = \text{base} \times \text{height} (the perpendicular height, not the slant side).
Area of a rhombus = \tfrac12 \times (\text{product of its diagonals}).
Area of a trapezium = \tfrac12 \times \text{height} \times (\text{sum of the parallel sides}).
These special formulas all flow from dissection, reshaping a figure into a rectangle of equal area, a method from the ancient Śulba-Sūtras.
To convert areas between units, the length factor is squared: 1\text{ in}^2 = 6.4516\text{ cm}^2, 1\text{ ft}^2 = 144\text{ in}^2, 1\text{ km}^2 = 1{,}000{,}000\text{ m}^2, 1\text{ acre} = 43{,}560\text{ ft}^2.