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Example Questions
Example Question #3 : Other Polygons
Polygon is a regular nine-sided polygon, or nonagon, with perimeter 500. Which choice comes closest to the length of diagonal ?
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 #1 : 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 ?
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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