Area of an Obtuse Triangle Calculator

Enter the three side lengths of a triangle to find its area with Heron's formula, along with the perimeter, largest angle, and whether the triangle is acute, right, or obtuse.

Quick Facts

Heron's formula
Area = √(s(s−a)(s−b)(s−c))
s is the semi-perimeter, (a+b+c)/2 — no height or angle needed.
Obtuse triangle
Exactly one angle greater than 90°
That angle is always opposite the triangle's longest side.

Your Results

Calculated
Area
-
Heron's formula, in square units
Perimeter
-
Sum of the three sides
Largest angle
-
Opposite the longest side
Triangle type
-
Acute, right, or obtuse

Ready

Enter the three side lengths, then press Calculate.

Formula and method for the Area of an Obtuse Triangle Calculator

Area of an Obtuse Triangle (Heron's Formula):

A = √(s(s−a)(s−b)(s−c))

where s = (a + b + c) / 2 is the semi-perimeter

An obtuse triangle is any triangle with one interior angle greater than 90°. Its area is found the same way as any other triangle — "obtuse" describes its shape, not a different formula. Given the three side lengths a, b, and c, Heron's formula finds the area directly, without needing to measure a height or an angle.

How the calculation works

First, the semi-perimeter s is found by adding the three sides and dividing by two: s = (a + b + c) / 2. That value feeds into Heron's formula, A = √(s(s−a)(s−b)(s−c)), to give the area. Separately, the calculator applies the law of cosines to find the triangle's largest angle — the one opposite the longest side — and reports whether that angle makes the triangle acute (all angles under 90°), right (exactly 90°), or obtuse (over 90°).

Common mistakes

  • Ignoring the triangle inequality: the two shorter sides must add up to more than the longest side, or no triangle exists. Sides of 3, 4, and 10 cannot form a triangle because 3 + 4 = 7 is less than 10.
  • Mixing units: all three sides must be measured in the same unit before entering them — mixing inches and feet produces a meaningless area.
  • Assuming the obtuse angle has to be measured directly: it doesn't — in every triangle, the largest angle is always opposite the longest side, so identifying the longest side and applying the law of cosines is enough to locate it.

Real-world applications

  • Land surveying and plot boundaries often form non-right triangles; Heron's formula finds the area from measured side lengths alone.
  • Roof framing, trusses, and gusset plates frequently involve obtuse angles where edge lengths are easier to measure on site than angles.
  • Navigation and construction triangulation use the same side-length-to-area relationship to cross-check measurements.
  • Geometry and trigonometry coursework use obtuse triangles to illustrate the law of cosines and Heron's formula together.

Frequently Asked Questions

What is the formula for the area of an obtuse triangle?
The area of any triangle, including an obtuse one, can be found from its three side lengths using Heron's formula: A = √(s(s−a)(s−b)(s−c)), where s = (a + b + c) / 2 is the semi-perimeter. This works the same way whether the triangle is acute, right, or obtuse.
How do I know if a triangle is obtuse?
A triangle is obtuse when one interior angle is greater than 90°. Using the law of cosines, the angle opposite the longest side c is obtuse when c² is greater than a² + b². This calculator finds the largest angle automatically and reports whether the triangle is acute, right, or obtuse.
Do the three side lengths need to satisfy a rule?
Yes. Any two sides must add up to more than the third side — the triangle inequality. If a + b ≤ c for any arrangement of the sides, no triangle can be formed, and the calculator flags the input as invalid.
What units does the result use?
The calculator works with any consistent unit of length. Enter side lengths in centimeters and the area comes out in square centimeters; enter feet and the area comes out in square feet, and so on.

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