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
Perimeter of an Equilateral Triangle Perimeter of an Isosceles Triangle Perimeter of a Scalene Triangle
Equilateral Triangle Isosceles Triangle Scalene Triangle

Area of a Triangle

Area of Triangle

Formula for Area of a Triangle

Example

Find the area and perimeter of the following triangle:

Area of a Triangle

P = 2 · 11 + 7.5 = 29.5 cm

Triangle Operations

Square

Square

Perimeter of a Square Formula

Area of a Square Formula

Example

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

Square

A = 52 = 25 cm2

Rectangle

Rectangle

Rectangle Formula

Area of a Rectangle Formula

Example

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

Rectangle

P = 2 · (10 + 6) = 32 cm

A = 10 · 6 = 60 cm2

Rhombus

Rhombus

Rhombus Formula

Area of a Rhombus Formula

Example

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

Area of a Rhombus

P = 4 · 17 = 68 cm

Rhombus Operations

Rhomboid

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.

Rhomboid

P = 2 · (4.5 + 4) = 17 cm

A = 4 · 4 = 16 cm2

Area of a Trapezoid

Area of a Trapezoid

Formula for Area of a Trapezoid

Example

Calculate the area of the following trapezoid:

Area of a Trapezoid

Trapezoid Operations

Area of a Regular Polygon

Area of a Regular Polygon

Formula for Area of a Regular Polygon

n is the number of sides

Formula for Area of a Regular Polygon

Examples

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

Area of a Regular Polygon

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

Regular Pentagon Operations

Regular Pentagon Operations

Regular Pentagon Operations

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

Area of a Regular Hexagon

Regular Hexagon

Regular Hexagon Operations

P = 6 · 4 = 24 cm

Regular Hexagon Operations

Area of a Polygon

Area of an Irregular Polygon

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

A = T1 + T2 + T3 + T4

Examples

Calculate the area of the following polygon:

Area of a Polygon

P = 11 · 2 + 5 + 13 + 12 = 52 cm

AD = BC; AB = DC flecha Rhomboid

A = AR + AT

A = 11 · 12 + (12 · 5 ) : 2 = 162 cm2