# ACT Math : How to find the length of a side of a polygon

## Example Questions

### Example Question #3 : Other Polygons

Polygon  is a regular seven-sided polygon, or heptagon, with perimeter 500. Which choice comes closest to the length of diagonal ?

Explanation:

Congruent sides  and  and the diagonal  form an isosceles triangle.

, being an angle of a seven-sided regular polygon, has measure

The other two are congruent, and each has measure

The length of one side is one-seventh of 500, or

can be found using the Law of Sines:

Of the given choices, 130 comes closest.

### Example Question #1 : How To Find The Length Of A Side Of A Polygon

Polygon  is a regular nine-sided polygon, or nonagon, with perimeter 500. Which choice comes closest to the length of diagonal ?

Explanation:

Congruent sides  and  and the diagonal  form an isosceles triangle.

, being an angle of a nine-sided regular polygon, has measure

The other two are congruent, and each has measure

The length of one side is one-ninth of 500, or

can be found using the Law of Sines:

Of the given choices, 105 comes closest.

### Example Question #2 : How To Find The Length Of A Side Of A Polygon

What is the side length of a 12-sided polygon with a perimeter of