Class 9 • Maths • Chapter 10
HERON’S FORMULA
True & False Quiz
Semi-perimeter. Area. No Height.
✓True
✗False
25
Questions
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Ch.10
Chapter
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IX
Class
Why True & False for HERON’S FORMULA?
How this format sharpens your conceptual clarity
🔵 Heron's Formula provides a powerful method to find the area of any triangle when all three sides are known — no height required.
✅ T/F tests the formula itself, the semi-perimeter definition, and application to quadrilaterals split into triangles.
🎯 s is the SEMI-perimeter = (a+b+c)/2, not the full perimeter — a very common substitution error tested in T/F.
📋
Read each statement carefully. Click True or False — instant feedback with explanation appears. Submit anytime; unattempted questions are marked Skipped.
Q 1
Heron's formula is used to find the area of a triangle when all its sides are known.
Q 2
Semi-perimeter is half the perimeter of a triangle.
Q 3
Heron's formula works only for right-angled triangles.
Q 4
The formula for area using Heron's formula is \(A = \sqrt{s(s-a)(s-b)(s-c)}\).
Q 5
If the length of one side is equal to or greater than the sum of the other two, a triangle is always possible.
Q 6
The perimeter of a triangle is the sum of the lengths of all its sides.
Q 7
If sides are 3 cm, 4 cm, 5 cm, then the perimeter is 12 cm.
Q 8
To use Heron's formula, you must always know the height of the triangle.
Q 9
The semi-perimeter of a triangle with sides 6 cm, 8 cm, 10 cm is 12 cm.
Q 10
Heron's formula cannot be applied to an equilateral triangle.
Q 11
All triangles with integer sides can have integral area.
Q 12
Heron's formula is applicable only if we know at least two sides and the included angle.
Q 13
If a triangle has sides 7 cm, 10 cm, and 12 cm, the semi-perimeter is 14.5 cm.
Q 14
The largest side of a triangle is always opposite the largest angle.
Q 15
Heron’s formula uses square roots in its calculation.
Q 16
If the triangle is degenerate (all points on a straight line), Heron's formula gives zero area.
Q 17
If a = b = c, the triangle is always equilateral.
Q 18
Heron's formula can be derived from the law of cosines.
Q 19
The sum of any two sides of a triangle is always greater than the third side.
Q 20
To use Heron's formula, side lengths must be positive real numbers.
Q 21
If the area calculated using Heron’s formula is imaginary, the triangle does not exist.
Q 22
A triangle can be constructed with sides 1 cm, 2 cm, and 3 cm.
Q 23
Heron's formula can also be used to find the area of a quadrilateral.
Q 24
Area of triangle increases as the perimeter increases, for given side ratios.
Q 25
The practical use of Heron's formula is in finding areas of plots with triangular shapes.
Key Takeaways — HERON’S FORMULA
Core facts for CBSE Boards & exams
1
Semi-perimeter: s = (a + b + c) / 2.
2
Heron's Formula: Area = √[s(s−a)(s−b)(s−c)].
3
The formula works for ANY triangle — scalene, isosceles, equilateral.
4
For equilateral triangle with side a: Area = (√3/4)a² (derivable from Heron's).
5
A quadrilateral can be split into two triangles; apply Heron's to each and add areas.
6
If s = semi-perimeter, then s−a, s−b, s−c must all be POSITIVE for a valid triangle.