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

Parts

Side

Angle

Vertex

Properties

The sum of all the angles of a triangle is equal to 180°

The sum of the lengths of any two sides of a triangle is greater than the length of the third side

The difference between any two sides of a triangle is less than the length of the third side

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 cm^{2}

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(s–a)(s–b)(s–c), where s = ½ (a+b+c) In this triangle, s = ½ (3 cm + 4 cm+ 5 cm) = 6 cm Since, A= √s(s–a)(s–b)(s–c) = √6(6-3)(6-4)(6-5) = √36 = 6 cm^{2}

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

The differences between the types are given below:

Apart from the above three types, there is Equiangular Triangle with all three internal angles equal to 60°and thus have all sides equal similar to an Equilateral Triangle