### All High School Math Resources

## Example Questions

### Example Question #531 : Plane Geometry

What is the length of a diagonal of a regular hexagon with side length ?

**Possible Answers:**

**Correct answer:**

Regular hexagons are comprised of six equilateral triangles; in our question, these triangles each have side length 4 (see diagram).

The length of a diagonal is equal to two times the length of the side. In this instance, the answer is 8.

### Example Question #1 : How To Find The Length Of The Diagonal Of A Hexagon

How many diagonals are there in a regular hexagon?

**Possible Answers:**

**Correct answer:**

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 #3 : How To Find The Length Of The Diagonal Of A Hexagon

How many diagonals are there in a regular hexagon?

**Possible Answers:**

10

3

9

6

18

**Correct answer:**

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.

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