### Overview:

Before starting, I would like to explain the term **“area of Triangle”, **which is defined as the region occupied inside the boundary of a flat Triangle. Then, I want to introduce you to the Geometric Shape triangle and I will explain What do you mean by area of a triangle and Heron’s Formula? Moreover, I will demonstrate how to find the area of a triangle? Furthermore, I will write a logic and c program to find the area of the triangle with output. After all, I will explain the resultant output.

### Table of contents:

- What is a Triangle?
- What are the properties of the Triangle?
- What do you mean by the area of a triangle?
- Demonstration how to find area of a triangle.
- Define Heron’s Formula.
- Main Logic to find the area of a triangle.
- C program to find area of triangle
- Conclusion

### What is the Triangle?

A triangle is a three-sided polygon that consists of three edges and three vertices. If ABC is a triangle, then it is denoted as ∆ABC, where A, B and C are the vertices of the triangle and AB, BC, CA are the edges of the triangle. A triangle is a two-dimensional Geometric shape.

### What are the properties of the Triangle?

The properties of the triangle are as follows:

- The sum of all the angles of a triangle(of all types) is equal to 180°.
- The sum of the length of the two sides of a triangle is greater than the length of the third side.
- In the same way, the difference between the two sides of a triangle is less than the length of the third side.
- The side opposite the greater angle is the longest side of all the three sides of a triangle.
- The exterior angle of a triangle is always equal to the sum of the interior opposite angles. This property of a triangle is called an exterior angle property.
- Two triangles are said to be similar if their corresponding angles of both triangles are congruent and lengths of their sides are proportional.

### What do you mean by the area of a triangle?

The area of a triangle given 3 sides is the region enclosed by its perimeter or the three sides of the triangle. The standard unit for measurement of the area is meter^{2}. In general area of the triangle is calculated as follows:

- The “Heron’s Formula” for the area of the triangle: √(s*(s-a)*(s-b)*(s-c));

### Where,

s is a semi parameter.

a, b and c are the edges of the triangle.

### Demonstration how to find area of a triangle:

### Define Heron’s Formula.

Heron’s formula includes two important steps as follows:

**Step 1:**Find the semi perimeter of a triangle by adding all the three sides of a triangle and dividing it by 2.**Step 2:**apply the semi-perimeter of triangle value in the main formula called “Heron’s Formula” to find the area of a triangle.

The main formula called “Heron’s Formula” to find the area of a triangle is as follows:

√(s × (s-a) × (s-b) × (s-c));

The measurement unit of the area of a triangle is a square unit.

### Main Logic to find the area of a triangle

**Step 1:**First of all declare 6 variables such as a, b,c for triangle sides, Perimeter P, semi perimeter s and Area.**Step 1:**User will enter the three sides of the triangle a, b, c.**Step 2:**Calculating the Perimeter of the Triangle using the formula P = a + b + c.**Step 3:**Calculating the semi perimeter using the formula (a + b + c)/2 and store it into variable s.**Step 4:**Calculating the Area of a triangle using Heron’s Formula: √(s × (s - a) × (s - b) × (s - c)); and store it into Area variable.**Step 4:**Print the variable area.

### C program to find area of triangle

/* C Program to find Area of a Triangle and Perimeter of a Triangle */ #include <stdio.h> #include <math.h> int main() { float a, b, c, P, s, Area; printf("\nPlease! Enter First edge of the triangle: "); scanf("%f",&a); printf("\nPlease! Enter Second edge of the triangle: "); scanf("%f",&b); printf("\nPlease! Enter Third edge of the triangle: "); scanf("%f",&c); P = a + b + c; s = (a + b + c)/2; Area = sqrt(s * (s - a) * (s - b) * (s - c)); printf("\n Perimeter of the Triangle = %.2f\n", Perimeter); printf("\n Semi Perimeter of the Triangle = %.2f\n",s); printf("\n Area of the triangle = %.2f\n",Area); return 0; }

**The output of the Program:**

### Conclusion

This Program accepts the three sides of the triangle a, b, c. Then, Calculates the Perimeter of the Triangle. Moreover, calculate the semi perimeter using the formula (a + b + c) / 2 and the Area of a triangle using Heron’s Formula: √(s × (s - a) × (s - b) × (s - c)). After the successful execution of the program the final area of a triangle is shown on screen.