Heron's formula
The area of any triangle from its three sides.
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Know all three sides of a triangle? Heron’s rule gives its area.
Look: A field with sides 13 m, 14 m and 15 m.
✏️ Your turn!
Type your answer and press Check. Kutty will tell you if it is right.
1Sides 3, 4, 5: area?
2Sides 5, 5, 6: area?
3Sides 6, 8, 10: s = ?
! Careful!
✗Using the whole perimeter for s.
✓s is half the perimeter.
✗Forgetting the square root.
✓The last step is √.
See the whole lesson on one page
Know all three sides of a triangle? Heron’s rule gives its area.
First find s, half of the perimeter. Then multiply s by (s − each side), and take the square root.
Think of it like thisA farmer can walk the three edges of a field with a tape, but cannot easily measure its height. Heron’s rule solves that.
- s
- Half of the perimeter.
Solved together
Find the area of a field with sides 13 m, 14 m and 15 m.
Half the perimeter.
s = (13 + 14 + 15) ÷ 2 = 21s minus each side.
21 − 13 = 821 − 14 = 721 − 15 = 6Multiply and take the square root.
21 × 8 × 7 × 6 = 7,056√7,056 = 84
AnswerArea = 84 m².
Now practise it
Kanakku makes new questions on heron's formula every time. It shows the working and gives a hint when you are stuck.