**Introduction**

** ** A triangle has three sides. Three intersecting lines are used to form the triangle. The total angle of the triangle is 180 degree.
Triangle has three angles and three vertices. Triangles are classified based on sides and angles. There are different formulas are used for solving the triangles. In solving triangle, pythagoras
theorem is used for finding the sides of the triangle. Based on sides triangles are classified as, isosceles triangle, equilateral triangle, and scalene triangle. Based on angles triangles are
classified as, right angle triangle, obtuse triangle, acute triangle.

**Formula for right angle triangle:**

Area of the right triangle is = (1 / 2) * b * h

Here, b = base and h = height

**Formula for finding side length:**

Using pythagoras theorem

A^{2} = B^{2} + C^{2}

Here, A = hypotenuse, B = opposite side, C = adjacent side

**Formula for equilateral triangle:**

Area of the equilateral triangle = √3 * (s / 2)^{2}

Here, s = side length.

**Using heron's formula:**

Area of the triangle = `sqrt(s (s - a) (s - b) (s - c))`

Here, s = (a + b + c) / 2, a, b, c are side length.

**Solving formulas for triangles example 1:**

Solve and find the area of the triangle with the base is 45 cm and height is 22 cm.

**Solution:**

Given base = 45 cm, height = 22 cm

**Formula:**

Area of the triangle = (1 / 2) * b * h

Substitute the given value in the above equation, we get

= (1 / 2) * 45 cm * 22 cm

= 495 cm^{2}

**Answer:**

The final answer is 495 cm^{2}

**Solving formulas for triangles example 2:**

Solve the given triangle problem. Two sides of the triangles are 15 cm and 20 cm. Find the third side of the triangle.

**Solution:**

Given two sides are B = 15 cm, C = 20 cm

**Formula:**

Using pythagoras theorem,

A^{2} = B^{2} + C^{2}

= 15^{2} cm + 20^{2} cm

= 625 cm

Take square root on both sides, we get

A = 25 cm

**Answer:**

The final answer is 25 cm

**Solving formulas for triangles example 3:**

Solve for finding area of the equilateral triangle with side length is 12 cm.

**Solution:**

Given side length s = 12 cm

**Formula:**

Area = √3 * (s / 2)^{2}

= √3 * (12 / 2)^{2}

= 10.39 cm^{2}

**Answer:**

The final answer is 10.39 cm^{2}