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Perimeters And Areas Of Plane Figures — Revision Notes

NIOS · Class 10 · Maths

Perimeters And Areas Of Plane Figures revision notes for NIOS Class 10 Maths: 4 topics in quick points. Part of the NIOS Class 10 Maths syllabus.

42 questions24 flashcards17 formulas & key relations5 concepts

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An infographic summarizing the perimeter and area formulas for common 2D geometric shapes like rectangles, squares, parallelograms, triangles, rhombuses, trapeziums, and circles. Each figure should be
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Key Topics to Revise

1

1. Core Formula Set for Plane Figures

  • Rectangle, square, triangle, parallelogram, rhombus, trapezium, circle, sector, and circular path are the main figures covered.
  • A rectangle uses perimeter 2(l+b) and area lb.
  • A square uses perimeter 4a, area a^2, and diagonal a√2.
2

2. Heron's Formula and Triangle Problems

  • Heron's Formula is used when the three sides of a triangle are known.
  • The semi-perimeter is not the perimeter; it is half of it.
  • Example with sides 5 cm, 6 cm, and 7 cm gives area 6√6 cm².
3

3. Rectangular Paths, Cross Paths, and Composite Rectilinear Figures

  • A rectangular path around a rectangle is found by outer area minus inner area.
  • For a path of width w around a rectangle of dimensions l × b, area = (l+2w)(b+2w) − lb.
  • Two cross paths through the middle of a rectangle have area w(l+b) − w².
4

4. Circles, Circular Paths, and Sector Formulas

  • The area of a circle is πr².
  • The circumference of a circle is 2πr.
  • Aryabhata (476–550 AD) gave π ≈ 62832/20000 = 3.1416.

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Full Notes

Key Concepts

Perimeter is the total lengthArea is the amount of surfaceFor a triangle with sidesA path around a rectangleFor a circle of radius r

Frequently Asked Questions

What are the important topics in Perimeters And Areas Of Plane Figures for NIOS Class 10 Maths?
Key topics in Perimeters And Areas Of Plane Figures include Core Formula Set for Plane Figures, Heron's Formula and Triangle Problems, Rectangular Paths, Cross Paths, and Composite Rectilinear Figures, Circles, Circular Paths, and Sector Formulas. Study these first, then practise questions on each for the NIOS Class 10 board exam.
How should I revise Perimeters And Areas Of Plane Figures for the NIOS Class 10 board exam?
Learn the core ideas first, then work through the 42 practice questions on Perimeters And Areas Of Plane Figures. Revise definitions regularly and use flashcards for quick recall before the exam.

Sources & Official References

Content is aligned to the official syllabus. Refer to the board website for the latest curriculum.

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