NCERT Solutions for Class 8th Maths Chapter 7 Area
Updated on 2026-09-19
About this chapter
Area is measured by counting unit squares. Perimeter is not a substitute — two regions can have the same perimeter and very different areas. Area of a triangle = ½ × base × height. It is proved by enclosing the triangle in a rectangle, and it holds even for obtuse triangles by subtracting one right triangle from another. Since any polygon splits into triangles, this one formula reaches every polygon. A parallelogram becomes a rectangle by one cut and one slide ( dissection ), which gives area = base × height. Any side may be used as the base, with its own height. A rhombus dissects into a rectangle whose sides are one diagonal and half the other, so area = ½ × product of the diagonals. A trapezium is half of the parallelogram made from two copies of it, so area = ½ × height × (sum of the p
- Rectangle and Squares
- Why Can't Perimeter be a Measure of Area?
- Triangles
- Some Applications of the Area Formula
- Triangles between Parallel Lines with a Common Base
- Area of any Polygon
- Parallelogram
- Rhombus
- Trapezium
- Finding the Area Using Two Copies of the Trapezium
Quick revision
| Figure | Area | What you must measure | Where it comes from |
|---|---|---|---|
| Rectangle | length × width | the two sidelengths | counting the unit squares packed inside |
| Right triangle | ½ × base × height | the two perpendicular sides | half of the rectangle on the same two sides |
| Any triangle | ½ × base × height | one side and the height to it | enclosing it in a rectangle of the same base and height |
| Any polygon | sum of the triangle areas | enough diagonals and heights | every polygon splits into triangles |
| Parallelogram | base × height | one side and its corresponding height | cut off one triangle and slide it across — a rectangle |
| Rhombus | ½ × d₁ × d₂ | the two diagonals | dissects into a rectangle of sides d₁ and ½d₂ |
| Trapezium | ½ × h × (a + b) | the height and both parallel sides | two copies make a parallelogram of base a + b |
| Region between two rectangles | outer area − inner area | both pairs of sidelengths | the path is what is left when the park is removed |
| Strip (tube) of width w | w × length of the middle line | the arm lengths and the width | straightening a bend loses w² at each corner |
| Unit change | 1 in² = 6.4516 cm²; 1 ft² = 144 in² | the length conversion | a length factor k scales area by k² |
Exercises
- In-text Questions — Rectangle and Squares Page 148
- In-text Question — Rectangle and Squares Page 149
- Why Can't Perimeter be a Measure of Area? — In-text Questions Page 150
- Figure it Out — Rectangle and Squares Page 150 – 152
- Triangles — In-text Questions Page 153
- Triangles — In-text Questions Page 154
- Some Applications of the Area Formula — In-text Questions Page 155
- Triangles between Parallel Lines with a Common Base — In-text Questions Page 156
- Triangles between Parallel Lines with a Common Base — In-text Questions Page 157
- Triangles — Figure it Out Page 157 – 159
- Area of any Polygon — In-text Questions Page 159
- Area of any Polygon — Figure it Out Page 160
- Parallelogram — In-text Questions Page 161
- Parallelogram — In-text Questions Page 162
- Parallelogram — Figure it Out Page 162 – 164
- Rhombus — In-text Question Page 164
- Rhombus — In-text Questions Page 165
- Trapezium — In-text Questions Page 166
- Trapezium — In-text Questions Page 167
- Finding the Area Using Two Copies of the Trapezium — In-text Questions Page 168
- Trapezium — Figure it Out Page 169 – 170
- Areas in Real Life — In-text Questions Page 170
- Areas in Real Life — In-text Questions Page 171