Skip to main content
Super TutorResources
Chapter 16 of 28
Syllabus

Area Theorems — Syllabus

ICSE · Class 9 · Mathematics

What Area Theorems covers in ICSE Class 9 Mathematics: 4 topics, for the 2026-27 session. Part of the ICSE Class 9 Mathematics syllabus.

35 questions25 flashcards3 formulas & key relations5 concepts

Interactive on Super Tutor

Studying Area Theorems? Get the full interactive chapter.

Quizzes, flashcards, AI doubt-solver and a step-by-step study plan — built for syllabus and more.

Try Super Tutor — Free

Free trial, no card needed.

An infographic showing the basic area formulas for a triangle, rectangle, and parallelogram, as a refresher before introducing area theorems.
Super Tutor

Learn better with visuals Super Tutor pairs illustrations like this with notes and quizzes for Area Theorems.

4 Topics · ICSE Class 9 Mathematics · 2026-27

Topics in Area Theorems

1

1. Basic ideas and figures between the same parallels

  • Area of a plane figure is the region bounded by it.
  • Figures with bases on one straight line and their other vertices on another line parallel to it are between the same parallels.
  • Such figures have equal altitude or height.
2

2. Theorem 19 and its corollary

  • Parallelograms on the same base and between the same parallels are equal in area.
  • In the proof, opposite sides of parallelogram ABCD are equal, so triangles ADF and BCE are congruent by ASA.
  • Congruent triangles are equal in area.
3

3. Theorem 20: area of a triangle and a parallelogram

  • The area of a triangle is half that of a parallelogram on the same base and between the same parallels.
  • In the proof, a parallelogram is constructed so that the given triangle has the same base and the same height as the parallelogram.
  • A diagonal of a parallelogram divides it into two equal-area triangles.
4

4. Theorem 21 and corollaries

  • Triangles on the same base and between the same parallels are equal in area.
  • In the proof, two parallelograms are constructed on the two triangles and their areas are shown equal using Theorem 19.
  • Each triangle is half of its constructed parallelogram.

Key Concepts

Central concept: Comparing and relating areas of parallelograms and triangles under special geometric conditions

Equal figuresFigures between the same parallelsTheorem 19Corollary to Theorem 19Theorem 20Theorem 21Corollaries to Theorem 21Equal area and altitude

Work through every topic in Area Theorems with notes and quizzes

Start This Chapter

Frequently Asked Questions

What are the important topics in Area Theorems for ICSE Class 9 Mathematics?
Key topics in Area Theorems include Basic ideas and figures between the same parallels, Theorem 19 and its corollary, Theorem 20: area of a triangle and a parallelogram, Theorem 21 and corollaries. Study these first, then practise questions on each for Class 9 exams.
How should I revise Area Theorems for Class 9 exams?
Learn the core ideas first, then work through the 35 practice questions on Area Theorems. 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.

More resources for Area Theorems

All ICSE Class 9 Mathematics Syllabus

For serious students

Get the full Area Theorems chapter — start free.

Quizzes, flashcards, an AI doubt solver and a study plan for ICSE Class 9 Mathematics. Free to start, no card needed.

Try Super Tutor Free
Try this chapter free