All ACT Math Resources
Example Questions
Example Question #4 : Other Polygons
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 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 : 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 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 : Other Polygons
What is the side length of a 12-sided polygon with a perimeter of
To find the side length, , of an -sided polygon with a perimeter of .
Use the formula: