## What is the Triangle Formula?

### What is a Triangle?

A polygon with three sides and three vertices is a triangle. In geometry, it is one of the fundamental topics of geometry. A triangle with vertices A, B, and C, is represented as △ ABC. In Euclidean geometry, any three non-collinear points determine a unique triangle and a unique plane at the same time. In a triangle, three angles are there. Each angle is formed when any two sides of the triangle meet at a common point, known as the vertex.

### Perimeter of Triangle Formula

The perimeter of any polygon is the sum of the lengths of the edges.

In the triangle,

Perimeter = The sum of the three sides

### Area of a Triangle

The triangle’s area is the total region that is enclosed by the three sides of any particular triangle. It is equal to half of the height of the basic periods. Therefore, we have to know the base and height of it to find the field of a tri-sided polygon.

Let us find out the area of different types of triangles.

Area of Isosceles Triangle

In a triangle of isosceles, two sides are equal in length. Also equal to each other are the two angles opposite to the two equal sides.

In case base and height are given, we use the following formula:

A = ½ × height × base

If three sides are given :

A = ½[√(a

^{2}− b^{2}/4) × b]Using 2 sides of the triangle and an angle between them :

A = ½ × b × c × sin(α)

Using two angles between two sides and their length :

A = [c

^{2}× sin(β) × sin(α)/ 2 × sin(2π−α−β)]

Area of Scalene Triangle Formula

A scalene triangle is a type of triangle in which there are different side dimensions on all three sides. The three angles are therefore different from each other due to this.

A = ½ × height × base

Area of Equilateral Triangle Formula

There are all three sides of an equilateral triangle equal to each other. As a consequence, all the inner angles are equal degrees, i.e. each angle is 60°.

A = (√3)/4 × side^{2}

Where,

A is the area of the triangle.

a is the length of the triangle.

b is the base of the triangle.

c is the third side of the triangle.

h is the height of the triangle.

α and β are the angles between two sides.

### Solved Example

Determine a triangle area with a base of 12cm and a height of 10cm.

Solution:

Area of a triangle = ½ × height × base

= ½ × 12 × 10

= 6 × 10

= 60 cm^{2}

### Conclusion

Since a triangle is a three-sided polygon, therefore to find the perimeter of a triangle we have to find the sum of the three sides. Similarly to find the area of a triangle, we must first know about the lengths of the sides of the triangle.

1. What is the Formula for Finding a Triangle's Perimeter?

Solution: Perimeter of a triangle = a + b + c

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

2. How can you Find the Third Side of a Given Two Sides of a Triangle?

Solution: We can use the Pythagoras theorem to find the third side if two sides are given. It states that the square of the side on which the hypotenuse is located is equal to the sum of the square areas on the other two sides.