# Area and Perimeter of Polygons

**Perimeter**

The **perimeter** of a **polygon** is equal to the **sum** of the** length** of its **sides**.

**Area**

The **area** of a **polygon** is the measure of the region enclosed by the sides of a polygon.

#### Perimeter of a Triangle

Equilateral Triangle |
Isosceles Triangle |
Scalene Triangle |

### Area of a Triangle

#### Example

Find the area and perimeter of the following triangle:

P = 2 · 11 + 7.5 = **29.5 cm **

### Square

#### Example

Calculate the area and perimeter of a square with 5 cm sides.

A = 5^{2} = 25 cm^{2}

### Rectangle

#### Example

Calculate the area and perimeter of a rectangular with a base of 10 cm and a height of 6 cm.

P = 2 · (10 + 6) = 32 cm

A = 10 · 6 = 60 cm^{2}

### Rhombus

#### Example

Calculate the area and perimeter of a rhombus whose diagonals are 30 and 16 cm, and its side measures 17 cm.

P = 4 · 17 = 68 cm

### Rhomboid

P = 2 · (a + b)

A = b · h

#### Example

Calculate the area and perimeter of a rhomboid shape of 4 sides of 4.5 cm and a height of 4 cm.

P = 2 · (4.5 + 4) = 17 cm

A = 4 · 4 = 16 cm^{2}

### Area of a Trapezoid

#### Example

Calculate the area of the following trapezoid:

### Area of a Regular Polygon

n is the number of sides

#### Examples

Calculate the area and perimeter of a regular pentagon with sides of 6 cm.

By applying the Pythagorean theorem for one of the triangles, we obtain:

Calculate the area and perimeter of a regular hexagon inscribed in a circle of 4 cm radius.

P = 6 · 4 = **24 cm**

### Area of a Polygon

The area is obtained by triangulating the polygon and adding the area of these triangles.

A = T_{1 } + T_{2 } + T_{3 } + T_{4 }

#### Examples

Calculate the area of the following polygon:

P = 11 · 2 + 5 + 13 + 12 = 52 cm

AD = BC; AB = DC Rhomboid

A = A_{R } + A_{T}

A = 11 · 12 + (12 · 5 ) : 2 = 162 cm^{2}