NCERT Solutions Class 9 Maths Chapter 6 — Measuring Space: Perimeter and Area#

Chapter 6 focuses on measuring plane figures — the perimeter (distance around) and area (space enclosed). You will apply formulas for triangles, rectangles, parallelograms, and composite shapes, and use Heron’s formula to find the area of a triangle from its three sides.

exercise set 6.1 exercise set 6.2 exercise set 6.3 end-of-chapter exercises

Exercises#

  • Exercise Set 6.1 — Circumference, arc length, perimeters of sectors and composite shapes (8 questions)
  • Exercise Set 6.2 — Areas of triangles, trapeziums and rhombuses, Heron’s formula, equal-area proofs (11 questions)
  • Exercise Set 6.3 — Areas of sectors and segments, polygons inscribed in a circle (10 questions)
  • End-of-Chapter Exercises — Area models of identities, wheels, trapezium and kite formulas, lunes and fitting shapes (27 questions)

What you will learn#

  • Circumference, arc length and the perimeter of sectors and composite shapes.
  • Areas of triangles, trapeziums and rhombuses, including Heron’s formula.
  • Areas of sectors, quadrants and segments.
  • Proofs about equal areas, and comparing inscribed polygons with circles.

Key formulas and results#

  • Heron’s formula: area $= \sqrt{s(s - a)(s - b)(s - c)}$, where $s = \dfrac{a + b + c}{2}$.
  • Area of a sector: $\dfrac{\theta}{360°} \times \pi r^2$; arc length: $\dfrac{\theta}{360°} \times 2\pi r$.

Read and revise#

Frequently asked questions#

How many exercises are in Class 9 Maths Chapter 6?
Three exercise sets — 6.1 (8 questions), 6.2 (11 questions) and 6.3 (10 questions) — plus 27 end-of-chapter exercises. Every question is solved step by step here.
When should you use Heron's formula?
When you know all three sides of a triangle but not its height. For a right triangle, half the product of the two shorter sides is quicker.

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