Triangle Area (SAS) Calculator
Calculate the area of any triangle using the side-angle-side (SAS) method. Enter two sides and the included angle for instant results using the formula A = 1/2ab sin(C) with our free calculator.
About This Calculator
The triangle area (SAS) calculator computes the area of a triangle when you know the lengths of two sides and the measure of their included angle. This side-angle-side method is one of the most common ways to determine triangle area in geometry, trigonometry, construction, and land surveying.
The formula used is A = 1/2 x a x b x sin(C), where a and b are the side lengths and C is the included angle in degrees. This formula is derived from the general triangle area formula A = 1/2 x base x height, where the height is expressed as b x sin(C) when a is taken as the base.
Simply enter two side lengths and the angle between them to get the area in square units matching your input units. This calculator is useful for students learning trigonometry, professionals in architecture and engineering, and anyone who needs to quickly compute triangle area from limited measurements.
Frequently Asked Questions
What is the SAS side-angle-side method for triangle area?
The SAS (side-angle-side) method calculates the area of a triangle when you know the lengths of two sides and the measure of the included angle. It uses the formula A = 1/2ab sin(C), where a and b are the side lengths and C is the included angle in degrees.
What is the formula for calculating triangle area with SAS?
The formula is A = 1/2 x a x b x sin(C), where a and b are the lengths of the two known sides and C is the included angle in degrees. The result is in square units matching the input units.
What units should I use for the side lengths?
You can use any consistent units for side lengths such as inches, feet, centimeters, or meters. The area result will be in the corresponding square units. For example, sides in meters produce area in square meters.
Can I use this calculator for any triangle?
This calculator works for any triangle where you know two sides and the included angle. If you know two angles and a side (ASA or AAS), or all three sides (SSS), you will need a different calculator.
What if the included angle is greater than 180 degrees?
In a triangle, the included angle must be between 0 deg and 180 deg (exclusive). The sine of angles between 0 deg and 180 deg is positive, so the area will always be positive. If the angle is exactly 0 deg or 180 deg, the area is zero since the sides would be collinear.
How accurate are the SAS triangle area results?
The calculator uses standard JavaScript floating-point arithmetic and provides results rounded to two decimal places. For most practical purposes including construction, geometry problems, and land measurement, this level of accuracy is sufficient.
Is this SAS triangle area calculator free to use?
Yes, all calculators on Calculy are completely free to use with no limits, registration, or hidden fees.