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

Study concepts, example questions & explanations for ACT Math

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Example Questions

Example Question #3 :Other Polygons

Polygonis a regular seven-sided polygon, orheptagon, with perimeter 500. Which choice comes closest to the length of diagonal?

Possible Answers:

Correct answer:

Explanation:

Congruent sidesandand the diagonalform 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 #4 :Other Polygons

Polygonis a regular nine-sided polygon, ornonagon, with perimeter 500. Which choice comes closest to the length of diagonal?

Possible Answers:

Correct answer:

Explanation:

Congruent sidesandand the diagonalform 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 #5 :Other Polygons

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

Possible Answers:

Correct answer:

Explanation:

To find the side length,, of an-sided polygon with a perimeter of.

Use the formula:

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