# Triangle

## Definition

In geometry, a triangle is a plane figure that is enclosed by three line segments.

• Side
• Angle
• Vertex

## Properties

1. The sum of all the angles of a triangle is equal to 180°
2. The sum of the lengths of any two sides of a triangle is greater than the length of the third side
3. The difference between any two sides of a triangle is less than the length of the third side
4. An exterior angle of a triangle is equal to the sum of its interior opposite angles. This is called the exterior angle property of the triangle

## Formulas

### Area of a Triangle

It is the total space enclosed by the triangle. The formula is given below:

Problem: Finding the area of a triangle when the BASE and HEIGHT are known

Find the area of a triangle whose base is 6 cm and height is 4 cm?

As we know,
A= ½ (b × h)
= ½ (6 × 4) cm
= 12 cm2

Problem: Finding the area of a triangle when only SIDES are known

Find the area of a triangle whose three sides are 3 cm, 4 cm, and 5 cm.

Here we will use the Heron’s formula,
A = √s(sa)(sb)(sc), where s = ½ (a+b+c)
In this triangle, s = ½ (3 cm + 4 cm+ 5 cm) = 6 cm
Since, A= √s(sa)(sb)(sc)
= √6(6-3)(6-4)(6-5)
= √36
= 6 cm2

### Perimeter of a Triangle

It is the distance covered around the edges of a triangle or simply the length of the boundary covered. The formula is given below:

Find the perimeter of a triangle whose three sides are 4 cm, 6 cm, and 8 cm

As we know,
P = a + b + c, where a, b, c are the measure of three sides
= 4 cm + 6 cm + 8 cm
= 18 cm

## Types

Triangles are classified into two groups: based on sides, 1) scalene, 2) isosceles, and 3) equilateral triangles; based on angles, 1) acute angle, 2) obtuse angle, and 3) right or right-angled triangles.

The differences between the types are given below: