The semiperimeter of a triangle is a fundamental geometric property that plays a significant role in various mathematical calculations and formulas involving triangles.

## Semiperimeter Calculator

## Introduction:

The semiperimeter of a triangle is a fundamental geometric property that plays a significant role in various mathematical calculations and formulas involving triangles. It is defined as half of the perimeter of the triangle. Calculating the semiperimeter is crucial in determining other properties of a triangle, such as its area, inradius, and circumradius. This semiperimeter calculator provides a quick and efficient way to compute the semiperimeter of any triangle.

**Instructions:**

To use the semiperimeter calculator, follow these simple steps:

1. Enter the lengths of the three sides of the triangle into the corresponding fields.

2. Click on the “Calculate” button.

3. The semiperimeter of the triangle will be displayed instantly.

Formula:

The formula to calculate the semiperimeter (s) of a triangle with side lengths a, b, and c is:

**s = a + b + c/2**

where:

a, b, and c are the lengths of the three sides of the triangle.

Example:

Suppose you have a triangle with side lengths of a = 5, b = 7, and c = 9. Using the semiperimeter calculator:

**s = 5 + 7 + 9/2 = 21/2 = 10.5**

Thus, the semiperimeter of the triangle is 10.5 units.

Application:

– Area of a triangle: The semiperimeter is used in Heron’s formula to calculate the area of a triangle.

– Inradius and Circumradius: Semiperimeter is involved in formulas for calculating the inradius and circumradius of a triangle.

– Triangle Inequality Theorem: This theorem states that the sum of the lengths of any two sides of a triangle must be greater than the length of the remaining side. Semiperimeter plays a role in verifying this theorem.

Note: Ensure that the lengths entered represent a valid triangle according to the Triangle Inequality Theorem.

This semiperimeter calculator provides a convenient tool for quickly finding the semiperimeter of any triangle, aiding in various geometric calculations and analyses.