Area of an Obtuse Triangle Calculator

When you only have the lengths of all three sides and no angle measurements, you can use Heron's formula. First, calculate the semi-perimeter by adding the three sides together and dividing by 2, which gives (10 + 17 + 25) / 2 = 26 inches. Next, subtract each side from the semi-perimeter: 26 - 10 = 16, 26 - 17 = 9, and 26 - 25 = 1. Multiply these differences together with the semi-perimeter (26 * 16 * 9 * 1 = 3,744). Finally, take the square root of that product (approximately 61.18) and multiply by 0.25, giving a final area of about 15.30 square inches.

If you know the lengths of two sides and the measure of the obtuse angle trapped between them, you can apply the side-angle-side area formula. Multiply the two side lengths together, multiply that result by the sine of the included angle, and then divide the final product by two. This trigonometric approach handles obtuse angles effortlessly because the sine function remains positive for angles between 0 and 180 degrees.

Technically, obtuse triangles can be categorized by their side lengths into two main types: obtuse scalene triangles, where all three sides and angles have different measurements, and obtuse isosceles triangles, where two sides are equal in length. Regardless of these classifications, every obtuse triangle shares the defining characteristic of having one interior angle that exceeds 90 degrees, forcing the altitude to fall outside the perimeter of the primary shape.

When you are given two angles and the included side, you can use the angle-side-angle area formula. First, find the third angle by subtracting the two known angles from 180 degrees (180 - 97 - 34 = 49°). Then, square the length of the known side (13 squared = 169), multiply it by the sine of both known angles, and divide by twice the sine of the sum of those two angles. This yields the exact surface area without needing to find the triangle's physical height.