# Area of Triangle Formula

## Formula

A triangle is a fundamental geometric shape with three sides and three angles. To calculate the area of a triangle, you can use the following formula:

Area = 1/2 x Base x Height

In this formula, "Base" represents the length of the base of the triangle (the bottom side), and "Height" represents the perpendicular distance from the base to the opposite vertex. The 1/2 factor is included because the area of a triangle is half the area of a rectangle with the same base and height.

## Examples

**Example 1:**

Calculate the area of a triangle with a base of 6 units and a height of 4 units.

Area = 1/2 x Base x Height

Area = 1/2 x 6 x 4 = 12 square units

The area of the triangle is 12 square units.

**Example 2:**

Find the area of a right triangle with a base of 9 inches and a height of 12 inches.

Area = 1/2 x Base x Height

Area = 1/2 x 9 x 12 = 54 square inches

The area of the right triangle is 54 square inches.

**Example 3:**

Determine the area of an equilateral triangle with a side length of 5 cm.

Since all sides of an equilateral triangle are equal, we can use the formula:

Area = (sqrt(3) / 4) x Side^2

Area = (sqrt(3) / 4) x 5^2 = (sqrt(3) / 4) x 25 = (25 * sqrt(3)) / 4 square cm

The area of the equilateral triangle is \( \frac{25\sqrt{3}}{4} \) square cm.