# Area and Perimeter of a Triangle

## Perimeter of a Triangle

The **perimeter of a triangle** equals the **sum** of the length of its three **sides**.

Equilateral Triangle |
Isosceles Triangle |
Scalene Triangle |

## Area of a Triangle

The **area of a triangle is equal to half its base times its height**.

The **height** of a triangle is each of the **perpendicular lines** drawn from one **vertex to the opposite side** (or its extension).

#### Example

Find the area of the triangle:

### Area of an Equilateral Triangle

#### Example

Calculate the area of an equilateral triangle with a side of 10 cm.

### Area of a Right Triangle

The area of a right triangle equals half the product of the legs.

#### Example

Calculate the area of the right triangle with legs measuring 3 and 4 cm.

### Semiperimeter

The semiperimeter of a triangle equals half the sum of its sides.

It is denoted with the letter **s**.

### Heron's Formula

Heron's formula is used to find the area of a triangle knowing the length of all three sides.

#### Example

Find the area of the triangle with sides measuring 3, 4 and 5 cm.

#### Circumscribed Circle in a Triangle

R = radius of the circumscribed circle.

#### Inscribed Circle in a Triangle

r = radius of the inscribed circle.

**s = semiperimeter**