Q:
# How Many Diagonals Does an Octagon Have?

**An octagon has 20 diagonals.** A shape's diagonals are determined by counting its number of sides, subtracting three and multiplying that number by the original number of sides. This number is then divided by two to equal the number of diagonals.

Credit:
Gareth Williams
CC-BY-2.0

The formula for finding the diagonals of a polygon with n-sides is n(n-3)/2. In the case of an octagon, n equals eight, and so the equation would be 8(8-3)/2.

A diagonal is the line that connects two vertices, or points where two sides connect. These lines can be used to divide a segment into pieces evenly and can help mathematicians better understand the way that various shapes work. Diagonals can also be used in reverse to help determine the sides of a particular shape. When drawing diagonals to a shape, the lines will never be on the same plane as the sides. The diagonals will never align with the lines and they will never touch the lines.

While it is possible to simply draw a shape and then draw diagonals through the shape, it is much easier to use the formula. Mathematicians developed this formula to help students, teachers and others easily determine the number of diagonals in a shape without the need to draw.

Learn more about Shapes-
Q:
## What Quadrilateral Has Perpendicular Diagonals?

A: The quadrilaterals that have perpendicular diagonals are "square," "rhombus" and "kite." A quadrilateral is a closed two-dimensional figure containing four... Full Answer >Filed Under: -
Q:
## What Is a Quadrilateral With Congruent Diagonals?

A: A quadrilateral with congruent diagonals is a rectangle or a square. All four angles of a rectangle and a square are right angles, making the diagonals con... Full Answer >Filed Under: -
Q:
## What Is a Convex Quadrilateral?

A: A convex quadrilateral is a four-sided figure with interior angles of less than 180 degrees each and both of its diagonals contained within the shape. A di... Full Answer >Filed Under: -
Q:
## How Many Diagonals Does a Pentagon Have?

A: A pentagon has five diagonals on the inside of the shape. The diagonals of any polygon can be calculated using the formula n*(n-3)/2, where "n" is the numb... Full Answer >Filed Under: