SAT Math : How to find the length of the diagonal of a hexagon
Study concepts, example questions & explanations for SAT Math
All SAT Math Resources
Example Questions
Example Question #1 : Hexagons
How many diagonals are there in a regular hexagon?
A diagonal is a line segment joining two non-adjacent vertices of a polygon. A regular hexagon has six sides and six vertices. One vertex has three diagonals, so a hexagon would have three diagonals times six vertices, or 18 diagonals. Divide this number by 2 to account for duplicate diagonals between two vertices. The formula for the number of vertices in a polygon is:
where 
Example Question #1 : Hexagons
How many diagonals are there in a regular hexagon?
18
9
6
3
10
9
A diagonal connects two non-consecutive vertices of a polygon. A hexagon has six sides. There are 3 diagonals from a single vertex, and there are 6 vertices on a hexagon, which suggests there would be 18 diagonals in a hexagon. However, we must divide by two as half of the diagonals are common to the same vertices. Thus there are 9 unique diagonals in a hexagon. The formula for the number of diagonals of a polygon is:
where n = the number of sides in the polygon.
Thus a pentagon thas 5 diagonals. An octagon has 20 diagonals.
Example Question #16 : Geometry
Hexagon 
Below is the referenced hexagon, with some additional segments constructed.
Note that the segments 
and
For the same reason, 
By the Pythagorean Theorem,
Certified Tutor
Certified Tutor
All SAT Math Resources
