HERON’S FORMULA - MCQs

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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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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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