Area of a triangle calculator
Enter the dimensions of a triangle and read off its area, its perimeter and the quantities that follow from them.
Area
26.832 816m²
- Perimeter
- 24
- Semi-perimeter
- 12
- Height onto side a
- 7.666 518 8
- Inradius
- 2.236 068
- Sides form a triangle
- 1
Show the working
- Side a = 7
- Side b = 8
- Side c = 9
- Area = sqrt(max((7+8+9)/2 * ((7+8+9)/2 - 7) * ((7+8+9)/2 - 8) * ((7+8+9)/2 - 9), 0)) = 26.8328
- Perimeter = 7 + 8 + 9 = 24
- Semi-perimeter = (7+8+9)/2 = 12
- Height onto side a = 7 > 0 ? 2*sqrt(max((7+8+9)/2 * ((7+8+9)/2-7) * ((7+8+9)/2-8) * ((7+8+9)/2-9), 0))/7 : 0 = 7.666 52
- Inradius = (7+8+9) > 0 ? sqrt(max((7+8+9)/2 * ((7+8+9)/2-7) * ((7+8+9)/2-8) * ((7+8+9)/2-9), 0)) / ((7+8+9)/2) : 0 = 2.236 07
- Sides form a triangle = (7+8>9 && 8+9>7 && 7+9>8) ? 1 : 0 = 1
Values are shown to six significant figures here; the arithmetic itself runs on exact fractions and is only rounded where a number is printed.
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The formula
- Heron's formula: area = sqrt(s(s-a)(s-b)(s-c)) with s the semi-perimeter
- inradius = area / s
If any side is longer than the other two combined the shape cannot close, and the validity row says so.
Lengths are entered in metres by default; switch any field to feet, inches or millimetres and the conversion is exact.