b c a h △1 △2 s=(a+b+c)/2 A=√s(s−a)(s−b)(s−c) Equilateral: (√3/4)a² 3-4-5, 5-12-13 triplets
√s(s-a)
Chapter 10  ·  Class IX Mathematics  ·  MCQ Practice

MCQ Practice Arena

Heron's Formula

Compute Area Without Height — Heron's Formula in Under 2 Minutes Every Time

📋 40 MCQs ⭐ 22 PYQs ⏱ 65 sec/Q
🚀 Start Practising 📖 Revise Notes First

MCQ Bank Snapshot

40Total MCQs
18Easy
16Medium
6Hard
22PYQs
65 secAvg Time/Q
5Topics
Easy 45% Medium 40% Hard 15%

Why Practise These MCQs?

CBSE Class IXState BoardsNTSE

Heron's Formula is the most formula-direct chapter in Class IX — every MCQ uses one formula (Area = √[s(s−a)(s−b)(s−c)]) applied to triangles, quadrilaterals, or composite polygons. CBSE awards 3–4 marks from this chapter; composite figure problems (quadrilateral split into two triangles) are the standard format. NTSE includes elegant area calculation problems. Mastering the formula and common Pythagorean triplets makes this chapter fast and reliable.

Topic-wise MCQ Breakdown

Semi-perimeter s6 Q
Heron's Formula for Triangle16 Q
Equilateral Triangle Area5 Q
Quadrilateral Area (Two Triangles)8 Q
Applications to Real-Life Figures5 Q

Must-Know Formulae Before You Start

Recall these cold before attempting MCQs — they appear in >70% of questions.

$s = (a+b+c)/2\ (\text{semi-perimeter})$
$\text{Area} = \sqrt{s(s-a)(s-b)(s-c)}$
$\text{Equilateral: Area} = \frac{\sqrt{3}}{4}a^2$
$\text{Isosceles shortcut: Area} = \frac{b}{4}\sqrt{4a^2-b^2}$
$\text{Quadrilateral: divide diagonal into two triangles}$

MCQ Solving Strategy

Step 1: Always compute s (semi-perimeter) first before anything else. Step 2: Calculate (s−a), (s−b), (s−c) separately and list them. Step 3: Multiply s(s−a)(s−b)(s−c) and take the square root. For quadrilateral MCQs, identify which diagonal divides it into two triangles, then apply Heron's formula to each triangle and add. Know the common Pythagorean triplets (3-4-5, 5-12-13, 8-15-17) — they appear frequently to give clean answers.

⚠ Common Traps & Errors

Difficulty Ladder

Work through each rung in order — do not jump to Hard before mastering Easy.

① Easy

Compute s, apply Heron's formula to basic triangles with integer sides

② Medium

Equilateral and isosceles triangle areas, quadrilateral with given diagonal

③ Hard

Quadrilateral where diagonal must be computed first, composite figures

★ PYQ

CBSE — quadrilateral area + composite; NTSE — elegant area applications

Continue Your Preparation

📖 Chapter Notes Revise concepts & theory 🧠 MCQ Practice Topic-wise Questions 📘✔️ Exercises Step-by-step NCERT solutions ✔️❌ True / False Concept-based True & False ➡ Next Chapter Surface Areas and Volumes
🎯 Knowledge Check

Maths — HERON’S FORMULA

50 Questions Class 9 MCQs
1
Heron’s formula is used to find the area of a triangle when we know:
2
The semi-perimeter of a triangle with sides 8 cm, 6 cm, and 10 cm is:
3
Heron’s formula for area of a triangle is:
4
If sides of a triangle are 7 cm, 8 cm, 9 cm, its semi-perimeter is:
5
Heron’s formula applies to:
6
For sides 3 cm, 4 cm, 5 cm, area using Heron’s formula is:
7
Semi-perimeter is represented by:
8
If a triangle has sides 15 m, 10 m, and 8 m, its semi-perimeter is:
9
The expression \(s-a\) represents:
10
Area of an equilateral triangle using Heron’s formula gives:
11
If \(s = 20\) cm and sides are 12, 14, and 18, then \(s-a\) equals:
12
Area of a triangle with sides 6, 6, 6 cm is:
13
Heron’s formula is also known as:
14
Semi-perimeter of triangle with sides 2.5 m, 3.5 m, 4 m is:
15
If sides are 9 cm, 12 cm, and 15 cm, which special triangle is it?
16
The term inside the square root in Heron’s formula is called:
17
For sides 13, 14, 15, find \((s-b)\):
18
Area of a triangle is always measured in:
19
Heron’s formula can also be used for finding the area of:
20
A triangle with sides 4, 5, and 6 has semi-perimeter:
21
The formula for area of equilateral triangle using Heron is:
22
Derivation of Heron’s formula uses:
23
If \(s-a=3,\, s-b=4,\, s-c=5\), then area is proportional to:
24
Maximum area is obtained when triangle is:
25
The term \((s-c)\) for sides 11, 14, 15 equals:
26
Heron’s formula involves how many multiplications inside square root?
27
Heron’s formula gives area even if triangle is:
28
For sides 2 m, 3 m, 4 m, the semi-perimeter is:
29
Lengths 2, 3, 6 cannot form a triangle because:
30
Heron’s formula includes a square root because:
31
What is the area of triangle with sides 5, 5, 6?
32
The Heron product is always:
33
If area computed by Heron’s formula is negative, mistake is in:
34
Heron’s formula helps in finding area when height is:
35
Sides 9, 10, 17 form:
36
Heron’s formula is most useful for:
37
Units of semi-perimeter are always:
38
Area of triangle becomes maximum when the triangle is:
39
If triangle has sides 12, 16, 20, the semi-perimeter is:
40
The area of triangle cannot be:
41
For sides 7 cm, 24 cm, 25 cm, triangle is:
42
Value of \(s-a\) must be:
43
Heron’s formula calculates:
44
A quadrilateral can be split into:
45
For sides 8,15,17 triangle is:
46
Semi-perimeter formula is:
47
Heron’s formula is helpful when the triangle is:
48
Area is always expressed in:
49
Sides of triangle must satisfy:
50
Area of triangle with sides 10, 10, and 12 cm is:
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Herons Formula | Mathematics Class 9 | Academia Aeternum
Herons Formula | Mathematics Class 9 | Academia Aeternum — Complete Notes & Solutions · academia-aeternum.com
Mastering Heron’s Formula is essential for every Class 9 learner, especially when solving problems based on triangles with known side lengths. This chapter not only strengthens conceptual understanding of triangle properties but also builds the foundation for advanced geometry in higher classes. To help students practice effectively, we have created 50 high-quality, exam-focused MCQs based strictly on NCERT Class IX Mathematics Chapter 10 – Heron’s Formula. These questions cover all…
🎓 Class 9 📐 Mathematics 📖 NCERT ✅ Free Access 🏆 CBSE · JEE
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Frequently Asked Questions

Heron’s Formula is a method to find the area of a triangle using only the lengths of its three sides. It does not require the height.

The formula was discovered by Heron (Hero) of Alexandria, an ancient Greek mathematician.

If sides are \(a, b, c\), then semi-perimeter: \(\displaystyle s = \frac{a + b + c}{2}\).

Area of triangle: \(\displaystyle \text{Area} = \sqrt{s(s-a)(s-b)(s-c)}\).

It helps find the area when the height is not known or difficult to measure, especially in scalene triangles.

Yes, it works for all types of triangles: scalene, isosceles, equilateral, acute, obtuse, and right triangles.

(1) Find semi-perimeter (s). (2) Calculate \(s-a, s-b, s-c\). (3) Multiply \(s(s-a)(s-b)(s-c)\). (4) Take square root to get area.

The sides must form a valid triangle: sum of any two sides > third side.

Divide the quadrilateral into two triangles, apply Heron’s Formula to each, then add the areas.

Yes. If each side is (a): \(s = \frac{3a}{2}\). Area becomes: \(\frac{\sqrt{3}}{4}a^2\).

The square root extracts the actual area from the product of semi-perimeter expressions.

Semi-perimeter simplifies the formula and ensures symmetry in the expression under the square root.

Usually: numerical area problems, word problems, quadrilateral divisions, or application-based questions.

For sides 3, 4, 5: \(s = 6\). Area = \(\sqrt{6 \times 3 \times 2 \times 1} = 6\).

\(s = 12\). Area = \(\sqrt{12 \times 5 \times 4 \times 3} = 12\sqrt{5}\).

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    HERON’S FORMULA — Learning Resources

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    ACADEMIA AETERNUM तमसो मा ज्योतिर्गमय · Est. 2025
    Sharing this chapter
    Herons Formula | Mathematics Class 9 | Academia Aeternum
    Herons Formula | Mathematics Class 9 | Academia Aeternum — Complete Notes & Solutions · academia-aeternum.com
    Mastering Heron’s Formula is essential for every Class 9 learner, especially when solving problems based on triangles with known side lengths. This chapter not only strengthens conceptual understanding of triangle properties but also builds the foundation for advanced geometry in higher classes. To help students practice effectively, we have created 50 high-quality, exam-focused MCQs based strictly on NCERT Class IX Mathematics Chapter 10 – Heron’s Formula. These questions cover all…
    🎓 Class 9 📐 Mathematics 📖 NCERT ✅ Free Access 🏆 CBSE · JEE
    Share on
    WhatsApp
    Telegram
    X / Twitter
    Facebook
    Instagram
    Threads
    Pinterest
    LinkedIn
    Quora
    Discord
    Reddit
    Email
    academia-aeternum.com/class-9/mathematics/herons-formula/mcqs/ Copy link
    💡
    Exam tip: Sharing chapter notes with your study group creates a reinforcement loop. Teaching a concept is the fastest path to mastering it.

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