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NCERT Solutions for Ganita Prakash (Part 2) Chapter 7 Area

Updated on 2026-09-05

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?
  • – 152Section 7.1 Rectangle and Squares
  • Triangles
  • Some Applications of the Area Formula
  • Triangles between Parallel Lines with a Common Base
  • – 159Triangles
  • Area of any Polygon
  • Parallelogram
  • – 164Parallelogram
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Exercises

  1. In-text Questions — Rectangle and Squares Page 148
  2. In-text Question — Rectangle and Squares Page 149
  3. Why Can't Perimeter be a Measure of Area? — In-text Questions Page 150
  4. – 152Section 7.1 Rectangle and Squares — Figure it Out Page 150
  5. Triangles — In-text Questions Page 153
  6. Triangles — In-text Questions Page 154
  7. Some Applications of the Area Formula — In-text Questions Page 155
  8. Triangles between Parallel Lines with a Common Base — In-text Questions Page 156
  9. Triangles between Parallel Lines with a Common Base — In-text Questions Page 157
  10. – 159Triangles — Figure it Out Page 157
  11. Area of any Polygon — In-text Questions Page 159
  12. Area of any Polygon — Figure it Out Page 160
  13. Parallelogram — In-text Questions Page 161
  14. Parallelogram — In-text Questions Page 162
  15. – 164Parallelogram — Figure it Out Page 162
  16. Rhombus — In-text Question Page 164
  17. Rhombus — In-text Questions Page 165
  18. Trapezium — In-text Questions Page 166
  19. Trapezium — In-text Questions Page 167
  20. Finding the Area Using Two Copies of the Trapezium — In-text Questions Page 168
  21. – 170Trapezium — Figure it Out Page 169
  22. Areas in Real Life — In-text Questions Page 170
  23. Areas in Real Life — In-text Questions Page 171
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