Area of Obtuse Triangle
Calculate the area of an obtuse triangle from two sides and the included angle. Free online obtuse triangle area calculator with formula and instant results.
About This Calculator
About Obtuse Triangle Area Calculator
This calculator computes the area of an obtuse triangle using the Side-Angle-Side (SAS) formula. An obtuse triangle has one interior angle greater than 90 degrees. To use the calculator, enter the lengths of any two sides and the obtuse included angle between them (between 90° and 180°). The calculator will instantly compute the area and show a step-by-step breakdown of the calculation.
Formula
The area is calculated using the standard SAS triangle area formula:
Area = ½ × a × b × sin(C)
where a and b are side lengths and C is the included obtuse angle in degrees. This formula works for any triangle when you know two sides and the included angle, but this calculator validates that angle C is in the obtuse range (90°-180°).
Frequently Asked Questions
What is an obtuse triangle?
An obtuse triangle is a triangle that has one interior angle greater than 90 degrees (but less than 180 degrees). The other two angles are acute (less than 90 degrees). The side opposite the obtuse angle is the longest side of the triangle.
How do you calculate the area of an obtuse triangle?
The area of an obtuse triangle can be calculated using the SAS (Side-Angle-Side) formula: Area = 0.5 x a x b x sin(C), where a and b are the lengths of two sides, and C is the included obtuse angle between them in degrees.
What is the difference between an acute triangle and an obtuse triangle?
An acute triangle has all three interior angles less than 90 degrees. An obtuse triangle has exactly one interior angle greater than 90 degrees (and less than 180 degrees). A right triangle has exactly one 90-degree angle.
Can an obtuse triangle have a right angle?
No, an obtuse triangle cannot have a right angle. By definition, an obtuse triangle has exactly one angle greater than 90 degrees. If it also had a right angle, the sum of just those two angles would already exceed 180 degrees, which violates the triangle angle sum theorem.
What units should I use for the side lengths?
You can use any consistent unit for side lengths such as centimeters, meters, inches, or feet. The area will be calculated in the corresponding square units. For example, if you enter sides in meters, the area will be in square meters.
Is this obtuse triangle area calculator free to use?
Yes, all calculators on Calculy are completely free to use. No registration, download, or payment is required. You can use the obtuse triangle area calculator as many times as you need for your geometry problems.
What is the angle range for an obtuse triangle?
In an obtuse triangle, the obtuse angle must be greater than 90 degrees and less than 180 degrees. The other two angles must be acute (between 0 and 90 degrees) and together they sum to less than 90 degrees since the total of all three angles is always 180 degrees.
How does the calculator verify the triangle is obtuse?
The calculator checks that the entered angle C is between 90 and 180 degrees. If angle C is 90 degrees or less, the triangle would be right or acute, not obtuse. If it is 180 degrees or more, the angle is invalid for any triangle.