Calculate the area and perimeter of different types of triangles using various formulas. Select the triangle type and calculation method, enter the known values, and get instant results with detailed steps.
Calculations are for informational purposes. Verify results for critical applications.
A triangle is a fundamental polygon in geometry with three edges and three vertices. The calculation of its area and perimeter depends on the known properties, such as side lengths and angles. This calculator supports various methods for different types of triangles.
Perimeter is the total length of the triangle's boundary, calculated by summing its three side lengths (P = a + b + c). Area is the space enclosed by the triangle.
Common area formulas include: Base and Height (A = 1/2 * b * h), which is universal but requires knowing the height. Heron's Formula, which uses the three side lengths, is ideal for scalene triangles. The SAS (Side-Angle-Side) formula (A = 1/2 * ab * sin(C)) is useful when two sides and the included angle are known.
The calculator also validates your inputs to ensure they can form a valid triangle. According to the Triangle Inequality Theorem, the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. Additionally, the sum of a triangle's internal angles must always be 180°.
Choose a triangle type and calculation method below to see the required inputs and the specific formula used for the calculation, including step-by-step solutions.