Enter the lengths of the three sides of the triangle below to calculate its semiperimeter and area using Heron's Formula.
Semiperimeter:
0
Area:
Compute a triangle's area using the lengths of its three sides by first finding the semiperimeter and then applying Heron's formula.
Key formula: Area = sqrt(s(s - a)(s - b)(s - c)), where s = (a + b + c) / 2
Area = sqrt(s(s - a)(s - b)(s - c)), where s = (a + b + c) / 2
Example with side lengths a = 7, b = 8, and c = 5.
s = (7 + 8 + 5) / 2 = 10
s - a = 3, s - b = 2, s - c = 5
10 × 3 × 2 × 5 = 300
Area = sqrt(300) ≈ 17.32
If the side lengths violate the triangle inequality, the expression under the square root becomes non-positive and the triangle is invalid; the calculator should indicate an error.
The area is reported in square units corresponding to the side length units you enter (for example, meters → m², centimeters → cm²).
Yes. Enter positive decimal values directly; the calculator accepts real numbers for side lengths.
For extreme magnitudes, floating-point rounding can affect precision. If needed, rescale units or use higher-precision arithmetic to improve accuracy.
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