How do you find the area of an obtuse triangle?

It's like any other triangle. The formula doesn't change for obtuse angles either. If the base and height are known, then the area is half of the product of the base and height. If all three sides are known, use Heron's Formula. If two sides and the angle between them are known, then the area is half of the product of those two sides multiplied by the sine of that angle. Pick the method that matches your measurements and the tool will do the calculation for you.

How do you find the area of an obtuse triangle with sides 10, 17 and 25?

We use Heron's formula. The semiperimeter is (10 + 17 + 25) / 2 = 26. The area is the square root of 26 * (26 - 10) * (26 - 17) * (26 - 25), which is the square root of 26 * 16 * 9 * 1, approximately 61.19 square units. We know that this triangle is obtuse because the sum of squares of 10 and 17 is less than the square of 25.

Is there a special formula for finding the area of an obtuse triangle?

No. All standard formulas for calculating the area of a triangle can be used on obtuse triangles as well. The base-height method requires some care, however. In an obtuse triangle, the perpendicular height may lie outside the triangle, so measure to the line containing the base rather than along the base itself. The value "half the product of the base and the height" does not change.

How do I determine if my triangle is actually an obtuse triangle?

Compare the longest side with the other two sides. If the square of the longest side is greater than the sum of the squares of the other two sides then the opposite angle is more than 90 degrees and the triangle is an obtuse triangle. If they are equal it is a right triangle, if they are less it is an acute triangle. This tool will automatically do the determination if the input provides enough information to identify the whole triangle.

Can an obtuse triangle be equilateral or right?

No. An equilateral triangle has three 60-degree angles, and all of them are acute. A right triangle has one 90-degree angle, so neither can have an angle greater than 90 degrees. An obtuse triangle can only be either isosceles (two sides the same length) or scalene (three different side lengths).

Area of an Obtuse Triangle Calculator

Choose your method

What do you know about the triangle?

Choose which measurements you have; the calculator shows the matching fields and gives the area right away.

Base and height

Three sides

Two sides and the angle between them

Two angles and the side between them

Enter all three side lengths. Heron's formula gives the area, and the calculator also checks whether the triangle is actually obtuse.

Enter your measurements

Side a

Side b

Side c

Area

This is an obtuse triangle. Its largest interior angle, 133.96 deg (°), is greater than 90 degrees, and it sits opposite the longest side. The area is shown above.

Perimeter

Largest angle

Full triangle (all sides and angles)

The whole triangle behind the area: all three sides and interior angles, filled in for the three-sides, two-sides-and-angle, and two-angles-and-a-side methods.

Side a

Side b

Side c

Angle A (opposite a)

Angle B (opposite b)

Angle C (opposite c)

Triangle area

cm²

Sides a = 10 cm, b = 17 cm, c = 25 cm with interior angles 16.73 deg (°), 29.31 deg (°), 133.96 deg (°) (summing to 180 degrees). Area 61.19, perimeter 52.

Steps and chart

Show the step-by-step working

Walk through the formula that produced the area for the method you picked.

Show the angle chart

See the three interior angles side by side - the tallest bar is the obtuse angle.

An obtuse triangle is a triangle in which one of the angles is greater than 90 degrees. This calculator allows you to calculate the area of an obtuse triangle using four different methods: base and height, three sides, two sides and included angle, or two angles and side between them. You can choose the method that best suits your available measurements. Once you have selected a method and entered the values, the area will be calculated instantly.

What is an obtuse triangle?

A triangle is obtuse if one of its three angles is larger than 90 degrees. Since the sum of the three angles always equals 180 degrees, there can only be one such angle and it will always be the largest angle and opposite the longest side. The other two angles are acute angles. An obtuse triangle can either be a scalene or an isosceles triangle but never an equilateral triangle. This is because all three angles of an equilateral triangle each measure 60 degrees.

You can determine the type of triangle by its sides without having to measure the angles. Consider the longest side as c and compare the square of c with the sum of squares of other two sides.

a^2 + b^2 < c^2 \;\Rightarrow\; \text{obtuse} \qquad a^2 + b^2 = c^2 \;\Rightarrow\; \text{right} \qquad a^2 + b^2 > c^2 \;\Rightarrow\; \text{acute}

If the square of the longest side is greater than the sum of the squares of the other two sides, then the angle opposite that side is larger than 90 degrees and the triangle is obtuse. If you can identify the whole triangle with your chosen method, this tool will make that determination for you.

Four methods for calculating area of obtuse triangles.

Which formula is used depends only on the measured data. In an equilateral triangle all four area calculation methods are identical.

1. Base side and height:

This is the most direct formula. Pick any side as your base and measure the perpendicular height from that point to the opposite corner.

\text{Area} = \tfrac{1}{2} \times b \times h

In obtuse triangles the foot of the perpendicular outside the base side. So the height is measured to the line containing the base side and that line is extended if necessary. The formula remains unchanged.

2. Three sides (Heron's formula):

If the three sides are known, then the area can be calculated using Heron's formula, which does not require any angle measure. The semiperimeter of a triangle with sides a, b and c is given by s = (a+b+c)/2.

\text{Area} = \sqrt{s\,(s-a)(s-b)(s-c)}.

This tool will not only read out any angle but also determine if a triangle is obtuse as it uses an equivalent one line formula.

\text{Area} = \tfrac{1}{4}\sqrt{(a+b+c)(-a+b+c)(a-b+c)(a+b-c)}.

3. Two sides and included angle:

If two sides and the included angle are known, then the area is half the product of those two sides multiplied by the sine of that angle.

\text{Area} = \tfrac{1}{2}\, a\, b \, \sin(\gamma)

If this angle itself exceeds 90 degrees, it is immediately an obtuse triangle. The third side can be calculated using the cosine theorem: c = sqrt (a ^ 2 + b ^ 2 - 2ab cos gamma).

4. Two angles and the side between them:

If you know two angles and the side between them, that's enough. The third angle is just 180 degrees minus the other two.

\text{Area} = \frac{a^2 \,\sin(\beta)\,\sin(\gamma)}{2\,\sin(\beta + \gamma)}

Here "a" is the side between the beta and gamma angles. If the third angle is known, then the remaining two sides can be calculated using the law of sines.

Example calculation:

The three sides are 10, 17 and 25. The longest side is 25, and the sum of the squares of 10 and 17 is 100 + 289 = 389. Since the square of 25 is less than 625, this is an obtuse triangle. By Heron's formula, half the perimeter is 26, and the area is the square root of the product of 26, 16, 9 and 1, which is approximately 61.19 square units.

The two angles are 97 degrees and 34 degrees, with the side length between them being 13 units long. The third angle is 180 - 97 - 34 = 49 degrees. Since there's a 97 degree angle this is already an obtuse triangle. Plugging these values into the area formula gives us 13 squared, times sin(97), times sin(34) divided by twice sin(131), which works out to approximately 62.14 square units.

You know	Formula	Example	Area
Base and height	half x b x h	b = 20, h = 6	60
Three sides	Heron's formula	10, 17, 25	61.19
Two sides + angle	half x a x b x sin C	13, 8, angle 97 deg	51.61
Two angles + side	a^2 sinB sinC / 2 sin(B+C)	97 and 34 deg, side 13	62.14

How to use this calculator:

Select the method above. The required fields will appear directly below and the area will be updated in real time as you enter values. For lengths millimeters, centimeters, meters, inches, feet, and yards can be used, and for angles degrees, radians, and gradians can be used. You can also change the units for each field at any time.

There are three methods to fully identify a triangle. The results will be color-coded to show if it is obtuse, right or acute. At the same time, the largest angle, perimeter as well as individual sides and angles will also be shown. As the individual angles cannot be determined by base and height alone, area will only be shown in this mode.

Types of obtuse triangles:

There are two types that you should know about. An obtuse isosceles triangle has two equal sides and two acute angles of the same size with the obtuse angle between those two equal sides. An obtuse scalene triangle has three unequal sides and three unequal angles, one of which is greater than 90 degrees. There are no obtuse right triangles or obtuse equilateral triangles because a triangle can only have one angle that is larger than 90 degrees.

Symbols used:

Symbol	Meaning	Example
a, b, c	The three side lengths	10, 17, 25
b, h	Base and its perpendicular height	20, 6
A, B, C	Interior angles opposite a, b, c	16.73, 29.31, 133.96 deg
gamma	The included angle between two sides	97 deg
s	Semiperimeter (a + b + c) / 2	26

This calculator is for general information and educational purposes only. It assumes that the triangle is on a plane surface (Euclidean Plane), and will treat measurements which cannot form a valid triangle as such.

Frequently asked questions

How do you find the area of an obtuse triangle?: It's like any other triangle. The formula doesn't change for obtuse angles either. If the base and height are known, then the area is half of the product of the base and height. If all three sides are known, use Heron's Formula. If two sides and the angle between them are known, then the area is half of the product of those two sides multiplied by the sine of that angle. Pick the method that matches your measurements and the tool will do the calculation for you.
How do you find the area of an obtuse triangle with sides 10, 17 and 25?: We use Heron's formula. The semiperimeter is (10 + 17 + 25) / 2 = 26. The area is the square root of 26 * (26 - 10) * (26 - 17) * (26 - 25), which is the square root of 26 * 16 * 9 * 1, approximately 61.19 square units. We know that this triangle is obtuse because the sum of squares of 10 and 17 is less than the square of 25.
Is there a special formula for finding the area of an obtuse triangle?: No. All standard formulas for calculating the area of a triangle can be used on obtuse triangles as well. The base-height method requires some care, however. In an obtuse triangle, the perpendicular height may lie outside the triangle, so measure to the line containing the base rather than along the base itself. The value "half the product of the base and the height" does not change.
How do I determine if my triangle is actually an obtuse triangle?: Compare the longest side with the other two sides. If the square of the longest side is greater than the sum of the squares of the other two sides then the opposite angle is more than 90 degrees and the triangle is an obtuse triangle. If they are equal it is a right triangle, if they are less it is an acute triangle. This tool will automatically do the determination if the input provides enough information to identify the whole triangle.
Can an obtuse triangle be equilateral or right?: No. An equilateral triangle has three 60-degree angles, and all of them are acute. A right triangle has one 90-degree angle, so neither can have an angle greater than 90 degrees. An obtuse triangle can only be either isosceles (two sides the same length) or scalene (three different side lengths).

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Disclaimer: This calculator is provided for general informational and educational purposes only. Our calculators are under active development, and results may be inaccurate, incomplete, or unsuitable for your situation. Always verify the figures independently and seek advice from a qualified professional before relying on them. We make no warranties and accept no liability for any loss or decision arising from use of this tool.

References

Wikipedia: Acute and obtuse triangles
Definition and properties of obtuse triangles and the side-length test.
Math is Fun: Area of Triangles
The base-height, three-sides, and two-sides-and-angle area formulas.
Wikipedia: Heron's formula
Area of a triangle from its three side lengths.