Chapter 10 · Class IX Mathematics · NCERT Exercises

Heron's Formula — Exercises

Triangle & Quadrilateral Areas Without Height — Exercise 10.1 Solved

📂 1 Exercise 📝 6 Questions 🎓 Easy-Moderate

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Exercise Index

①

Exercise 10.1

Heron's formula; semi-perimeter; area of triangle; area of quadrilateral by splitting into triangles

6 Q Easy-Moderate

1 exercise file · 6 total questions

Chapter at a Glance

CBSE BoardsNTSE

5 Concepts

4 Formulas

Easy-Moderate Difficulty

5–6% Weightage

Before You Begin

Prerequisites

✓Area of triangle = ½×b×h
✓Pythagoras theorem
✓Basic algebraic simplification

Have Ready

🔧Calculator (for square roots)
🔧Rough work sheet
🔧Verification using ½bh when possible

Exercise Topic Map

Exercise 10.1 Compute s = (a+b+c)/2; substitute into Heron's formula; for quadrilateral: draw diagonal to split into 2 triangles; apply formula to each

Key Formulae — Recall Before Solving

\(s = \dfrac{a+b+c}{2} \quad \text{(semi-perimeter)}\)

\(\text{Area} = \sqrt{s(s-a)(s-b)(s-c)} \quad \text{(Heron's Formula)}\)

\(\text{Equilateral triangle: Area} = \dfrac{\sqrt{3}}{4}a^2\)

\(\text{Quadrilateral area} = \triangle_1 + \triangle_2 \text{ (split by diagonal)}\)

NCERT Solving Method

Step 1 — Always compute s (semi-perimeter) first; write it down explicitly. Step 2 — Compute (s−a), (s−b), (s−c) separately; then multiply s(s−a)(s−b)(s−c). Step 3 — Take the square root; simplify any perfect squares under the radical first. Step 4 — Quadrilateral: draw one diagonal to split into two triangles; find the diagonal using Pythagoras if not given. Step 5 — Verify: if height is available, cross-check with Area = ½ × base × height.