Math Tools
Triangle Calculator
Calculate triangle area, perimeter, semiperimeter, and triangle type using three sides or base and height.
Triangle Calculator
Calculate triangle area, perimeter, semiperimeter, and triangle type using either three sides or base and height.
Enter all three sides to calculate area, perimeter, semiperimeter, and triangle type.
Formulas
Area = 1/2 × base × height
Heron's Formula: Area = √(s(s-a)(s-b)(s-c))
Perimeter = a + b + c
Semiperimeter = (a + b + c) / 2
Results
Area
6
Perimeter
12
Semiperimeter
6
Triangle type
Scalene
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What this calculator does
This calculator can find triangle area from base and height, or solve a triangle from three sides using Heron's formula.
What is a triangle calculator?
A triangle calculator is a tool that helps you solve common triangle measurements quickly. Depending on the input method, it can find triangle area, perimeter, semiperimeter, and triangle type without requiring manual calculations.
This is useful for geometry homework, engineering, design, construction planning, and general measurement problems where you need fast and accurate triangle calculations.
Triangle formulas used in this calculator
Triangle area formula
Area = 1/2 × base × height
Heron's formula
Area = √(s(s-a)(s-b)(s-c))
Triangle perimeter formula
Perimeter = a + b + c
Triangle semiperimeter formula
Semiperimeter = (a + b + c) / 2
Triangle formula reference table
| Measurement | Formula | When to use it |
|---|---|---|
| Area with base and height | Area = 1/2 × base × height | Use when the triangle base and perpendicular height are known. |
| Area with three sides | Area = √(s(s-a)(s-b)(s-c)) | Use Heron's formula when all three side lengths are known. |
| Perimeter | Perimeter = a + b + c | Use to find the total distance around the triangle. |
| Semiperimeter | s = (a + b + c) / 2 | Use as an intermediate value in Heron's formula. |
Examples for triangle calculations using three sides
These example values show how triangle area and related measurements are calculated.
| Example | Area | Perimeter | Notes |
|---|---|---|---|
| Sides 3, 4, 5 | 6 | 12 | Scalene right triangle |
| Sides 5, 5, 6 | 12 | 16 | Isosceles triangle |
| Sides 6, 6, 6 | 15.588457 | 18 | Equilateral triangle |
How to calculate triangle area step by step
If you know the base and height, multiply them together and divide the result by 2. This is the most direct triangle area formula and works when the height is known.
If you know all three sides, first calculate the semiperimeter, which is half the perimeter. Then apply Heron's formula to find the area from the three side lengths.
A triangle calculator makes this faster because it automatically applies the correct formula and helps prevent mistakes in arithmetic and square root calculations.
How to find triangle perimeter and semiperimeter
The perimeter of a triangle is the total length around the shape. Add the three sides together to get the perimeter.
The semiperimeter is half of that total. It is especially useful in geometry because it is required in Heron's formula for triangle area.
These measurements are useful in construction layouts, land surveying, geometry proofs, and engineering calculations where side lengths and boundaries matter.
Triangle types explained
Equilateral
All three sides are equal in length.
Isosceles
Two sides are equal in length.
Scalene
All three sides have different lengths.
Triangle type comparison table
| Triangle type | Definition | Example side lengths |
|---|---|---|
| Equilateral triangle | All three sides are equal. | 6, 6, 6 |
| Isosceles triangle | Two sides are equal. | 5, 5, 6 |
| Scalene triangle | All three sides are different. | 3, 4, 5 |
Where a triangle calculator is useful
A triangle calculator is useful in geometry classes, drafting, engineering, roofing, carpentry, and land measurement. It can help when solving triangle problems manually would take too long or lead to errors.
It is also a practical tool for checking homework answers, confirming measurements, and learning how triangle formulas work in real-world situations.
Triangle calculator FAQ and common triangle formulas
How do you calculate the area of a triangle?
Use one-half multiplied by base multiplied by height. If all three sides are known, you can also use Heron's formula.
What is Heron's formula for a triangle?
Heron's formula calculates area from three sides using the semiperimeter: area = √(s(s-a)(s-b)(s-c)).
How do you find the perimeter of a triangle?
Add the three sides together. The result is the total distance around the triangle.
What is the semiperimeter of a triangle?
The semiperimeter is half the perimeter, calculated as (a + b + c) / 2.
Can this triangle calculator identify triangle type?
Yes. When three sides are entered, the calculator can classify the triangle as equilateral, isosceles, or scalene.
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