## Example Questions

### Example Question #1 : How To Find The Length Of A Diagonal 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 trapezoid. and . being angles of a nine-sided regular polygon, have measure The other two angles are supplementary to these: The length of one side of the nonagon is one-ninth of 500, so The trapezoid formed is below (figure NOT drawn to scale): Altitudes and to the base have been drawn, so      This makes 140 the best choice.

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

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 trapezoid. and . being angles of a seven-sided regular polygon, have measure The other two angles are supplementary to these: The length of one side is one-seventh of 500, so The trapezoid formed is below (figure NOT drawn to scale): Altitudes and to the base have been drawn, so      This makes 160 the best choice.

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