Diagonals of a Polygon

A diagonal of a polygon is a line segment that joins two nonconsecutive vertices.

Number of Diagonals of a Polygon

Number of Diagonals of a Polygon

4 · (4 − 3) : 2 = 2

Diagonals of a Square

5 · (5 − 3) : 2 = 5 6 · (6 − 3) : 2 = 9

Diagonals of a PentagonDiagonals of a Hexagon

Diagonal of a Square

Diagonal of a Square

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

Diagonal of a Square

Diagonal of a Square

Diagonal of a Square

Example

Calculate the length of the diagonal for the square with a side of 5 cm.

Diagonal of a Square

Diagonal of a Square

Diagonal of a Square

Diagonal of a Rectangle

Diagonal of a Rectangle

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

Diagonal of a Rectangle

Diagonal of a Rectangle

Example

Calculate the length of the diagonal of a rectangle of 10 cm base and 6 cm height.

Diagonal of a Rectangle

Diagonal of a Rectangle

Diagonal of a Rectangle