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Schooling · Class 8 · Mathematics · Area · Chapter on a page

CBSE Class 8 · Mathematics · NCERT Ganita Prakash Part-II

Area: chapter on a page

A cut of Shishya's notes for this chapter: the first paragraph of the introduction and the key ideas, formulas and facts, common mistakes and quick revision lists, word for word. Nothing is added or reworded; the worked examples are left out (they are on the chapter page).

About the notes: Written by Shishya's AI on 26 Sept 2026 from the chapter's title and class level, in Shishya's own words — not a copy or summary of the textbook. Read the official chapter for the book's own text, activities and exercises.

This note's current text has no applied fact-check on record.

Mind map

Drawn from the same notes by a fixed rule (no AI): each label is the item's own words — its bold term, its label before a colon, a short formula as written, or its first words.

Mind map of Area: Key ideas, Formulas and facts, Watch out forKey ideasThe area of a rectangle is length ×…A parallelogram can be thought of as…A triangle is exactly half of a…A rhombus is a special parallelogram…A trapezium has one pair of parallel…The height in any of these formulas…You can find the area of irregular…Formulas and factsArea of rectangle = length × breadthArea of square = side × side = side²Area of parallelogram = base ×…Area of triangle = (1/2) × base ×…Area of rhombus = (1/2) × d₁ × d₂…Area of trapezium = (1/2) × (a + b)…All area measurements are in square…Watch out forUsing the slant side instead of the…Forgetting to multiply by (1/2) when…Mixing up the diagonals of a rhombus…Adding all four sides of a trapezium…Writing the answer without square…Area
The mind map as a list
  • Key ideas
    • The area of a rectangle is length ×…
    • A parallelogram can be thought of as…
    • A triangle is exactly half of a…
    • A rhombus is a special parallelogram…
    • A trapezium has one pair of parallel…
    • The height in any of these formulas…
    • You can find the area of irregular…
  • Formulas and facts
    • Area of rectangle = length × breadth
    • Area of square = side × side = side²
    • Area of parallelogram = base ×…
    • Area of triangle = (1/2) × base ×…
    • Area of rhombus = (1/2) × d₁ × d₂…
    • Area of trapezium = (1/2) × (a + b)…
    • All area measurements are in square…
  • Watch out for
    • Using the slant side instead of the…
    • Forgetting to multiply by (1/2) when…
    • Mixing up the diagonals of a rhombus…
    • Adding all four sides of a trapezium…
    • Writing the answer without square…

What this chapter is about

This chapter builds on what you already know about finding areas of simple shapes like rectangles and squares. In Class 8, you move forward to learn how to calculate the area of more complex figures — quadrilaterals such as parallelograms, rhombuses, trapeziums and also triangles. You will see how these formulas connect to each other and to the basic rectangle formula you learned earlier.

Key ideas

  • The area of a rectangle is length × breadth. This simple idea is the foundation for all other area formulas in this chapter.
  • A parallelogram can be thought of as a slanted rectangle. Its area equals base × height, where the height is the perpendicular distance between the two parallel sides, not the slant side.
  • A triangle is exactly half of a parallelogram with the same base and height. So area of a triangle = (1/2) × base × height.
  • A rhombus is a special parallelogram with all sides equal. Its area can be found using its two diagonals: area = (1/2) × d₁ × d₂, where d₁ and d₂ are the lengths of the diagonals.
  • A trapezium has one pair of parallel sides. Its area = (1/2) × (sum of parallel sides) × height.
  • The height in any of these formulas is always measured perpendicular (at right angles) to the base, never along a slant.
  • You can find the area of irregular shapes by dividing them into triangles, rectangles or other known figures, then adding the areas.

Formulas and facts to remember

  • Area of rectangle = length × breadth
  • Area of square = side × side = side²
  • Area of parallelogram = base × height (height is perpendicular to the base)
  • Area of triangle = (1/2) × base × height
  • Area of rhombus = (1/2) × d₁ × d₂ (d₁ and d₂ are the two diagonals)
  • Area of trapezium = (1/2) × (a + b) × h (a and b are the parallel sides, h is the height between them)
  • All area measurements are in square units (cm², m², etc.)

Common mistakes

  • Using the slant side instead of the perpendicular height in parallelogram or triangle formulas → always measure height at right angles to the base.
  • Forgetting to multiply by (1/2) when finding the area of a triangle, rhombus or trapezium → check which formulas have the half in them.
  • Mixing up the diagonals of a rhombus with its sides → the diagonal formula uses the two lines that cross inside, not the four equal edges.
  • Adding all four sides of a trapezium instead of only the two parallel sides → only the parallel pair goes into the formula.
  • Writing the answer without square units → area is always in cm², m² or other squared units.

Quick revision

  • Parallelogram area = base × perpendicular height.
  • Triangle area = half of base × height.
  • Rhombus area = half the product of its two diagonals.
  • Trapezium area = half the sum of parallel sides × height.
  • Height is always perpendicular to the base, never slanted.
  • Always state area in square units.