Area of Oblique Triangle Calculator

Calculate the area of any oblique (non-right) triangle using SAS, SSS, or ASA methods. Find all sides, angles, perimeter, and heights.

Select Method & Enter Values

A B C a b c

Result

Area of Triangle
--
square units
Area--
Perimeter--
Sides
Side a--
Side b--
Side c--
Angles
Angle A--
Angle B--
Angle C--
Heights (Altitudes)
Height h_a--
Height h_b--
Height h_c--
Area = ½ · a · b · sin(C)

Understanding Oblique Triangles

An oblique triangle is any triangle that does not contain a right angle (90°). Oblique triangles can be either acute (all angles less than 90°) or obtuse (one angle greater than 90°). Unlike right triangles, they require the Law of Sines, the Law of Cosines, or specialized area formulas.

Method 1: SAS (Side-Angle-Side)

When two sides and the included angle are known, the area can be calculated directly:

Area = ½ · a · b · sin(C)

This is often the most straightforward method. The remaining side can be found using the Law of Cosines, and the remaining angles via the Law of Sines.

Method 2: SSS (Heron's Formula)

When all three sides are known, Heron's formula provides the area:

s = (a + b + c) / 2   (semi-perimeter)
Area = √[s(s-a)(s-b)(s-c)]

This elegant formula, attributed to Hero of Alexandria (c. 60 AD), requires only the three side lengths.

Method 3: ASA (Angle-Side-Angle)

When two angles and the included side are known, the third angle is found by subtraction, then sides are found via the Law of Sines:

C = 180° - A - B
a = c · sin(A)/sin(C),   b = c · sin(B)/sin(C)
Area = ½ · a · b · sin(C)

Law of Cosines

c² = a² + b² - 2ab · cos(C)

Law of Sines

a/sin(A) = b/sin(B) = c/sin(C)

Comparison of Methods

  • SAS is ideal when you know two sides and their included angle. It gives the area directly in one step.
  • SSS (Heron's) is best when all three sides are measured. It does not require any angle measurements.
  • ASA is used when angles are easier to measure than sides, common in navigation and astronomy.

Applications

  • Land Surveying: Calculating the area of irregular plots by dividing them into triangles.
  • Navigation: Determining distances and bearings when direct measurement is impossible.
  • Architecture: Computing areas of non-rectangular surfaces for materials estimation.
  • Physics: Resolving forces in non-perpendicular directions and calculating work done by angled forces.