Area Class 8 Notes Maths Part 2 Chapter 7

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Class 8 Maths Chapter 7 Area Play Notes

Class 8 Area Notes

This chapter explains how to measure area and derive formula for shapes like rectangles, triangles, parallelograms, rhombuses and trapeziums. It also shows how to find areas by dividing figures, using dissections and applying these ideas in real-life situations.

Area
Area is the measure of the surface covered by a region. It is measured by counting the number of unit squares that exactly cover the region. It is measured in square units, e.g.cm2², m² etc.

Area of a Rectangle
The area of rectangle is the amount of surface it covers. Area of a rectangle = Length × Breadth

Area of square
A square is a special rectangle in which all sides are equal. Area of square = Side × Side = (Side)²

Triangle
To find the area of any triangle, we place it inside a rectangle and use the relationship between them or a diagonal divides a rectangle into two congruent triangles
i. e. each triangle has exactly half the area of the rectangle.
Area of a triangle = \(\frac{1}{2}\) × Base × Height

• The formula is valid for all types of triangles (acute, obtuse, right angled).
• Triangles on the same base and between the same parallel lines have equal areas.
• A line joining a vertex to the mid-point of the opposite side divides a triangle into two triangles of equal area.

Area of any Polygon
Any polygon (a shape with many sides) can be divided into several triangles. By summing the areas of these triangles, we can find the total area of the polygon.

Parallelogram
A parallelogram is quadrilateral, whose opposite sides are parallel and equal.
A parallelogram can be cut and rearranged (dissection) to form a rectangle of equal area.

Area of parallelogram = Base × Height
Any side can be taken as the base and height is perpendicular distance between its two parallel lines.

Rhombus
A rhombus is a parallelogram with all four sides equal. Its diagonals bisect each other at right angles (perpendicular) because of these special properties, we can find the area using diagonals.

Here, AC and BD are the diagonals.
Area of rhombus = \(\frac{1}{2}\) × Product of the diagonals

Trapezium
A quadrilateral which has one pair of parallel sides is called trapezium.

Area of trapezium = \(\frac{1}{2}\) × Height × Sum of the parallel sides
A trapezium is called an isosceles trapezium if the non-parallel sides ola trapezium are equal in length.

Unit Conversions For Area

• 1 inch =2.54cm, so 1 in² =6.4516 cm²
• 1 foot = 12 inches, so 1 ft² = 144 cm²
• 1 metre = 100 cm, so 1 m² = 10000 cm²
• 1 kilometre = 1000 m, so 1 km² = 1000000 m²
• 1 acre = 43560 ft² (used for large land areas)