Heron's Formula
Heron's formula gives the area of a triangle when the lengths of all three sides are known.
In one line: Heron's formula starts with half the boundary.
Practice This ConceptUnderstand it
When perpendicular height is not given, first find the semi-perimeter, then use the product involving the three side differences. It is especially useful for scalene triangles.
Formula and rule
s = (a + b + c)/2; Area = √[s(s - a)(s - b)(s - c)].
Use when all three sides are known.
See it worked out
Follow the example line by line, then use the same method on new questions.
Worked example
- 1For sides 5 cm, 12 cm, 13 cm, s = 15.
- 2Area = √(15 × 10 × 3 × 2) = √900 = 30 cm².
Method you can reuse
Visual tip
A triangle labelled a, b, c is enough; no height is required for Heron's formula.
Check yourself
Answer the question in your head before opening the answer.
Try it yourself
For a triangle with sides 6 cm, 8 cm, and 10 cm, what is the semi-perimeter?
Think first, then show answerHide answer
Common wrong answer
Using 30 instead of 15 as s for sides 5, 12, 13 gives a wrong product because s must be half the perimeter.
Don't mix this up
Exam tip
Heron's Formula diagram
Open full screen to read every label clearly.
Write it in the exam
Each point is worth about one mark. Write point 1 for a 1-mark question and keep adding points as the marks go up.
How CBSE asks it
- 1
Enough for 1 mark
Heron's formula gives the area of a triangle when the lengths of all three sides are known.
- 2
Add for 2 marks
Example: For sides 13 cm, 14 cm, and 15 cm, s = 21 cm and area = √(21 × 8 × 7 × 6) = 84 cm².
- 3
Add for 3 marks
When perpendicular height is not given, first find the semi-perimeter, then use the product involving the three side differences.
Practice this concept with focused MCQs
Open the concept quiz intro first, review the test details, and then start a focused MCQ set from this concept only. Instant score and answer review are live now.
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