Question

this diagram shows how a regular polygon inscribed in a circle changes as the number, n, of sides of the polygon increases from 8 to 12. information about the inscribed polygon and the isosceles triangle formed in the interior of the polygon is listed. • the length of the triangle’s base is represented by s. • the perimeter of the polygon is represented by sn. • the lengths of the triangle’s legs are represented by r. • the height of the triangle is represented by h. as the number of sides of the polygon increases, which statements are true? select all the correct answers. a. the height of the triangle approaches the value of π. b. the perimeter of the polygon approaches the value of 2π. c. the area of the polygon approaches the area of the circle. d. the perimeter of the polygon approaches the circumference of the circle. e. the height of the triangle approaches the length of the radius of the circle.

Explanation:

• Option A: The height \( h \) approaches the radius \( r \), not \( \pi \). Incorrect.
• Option B: The perimeter approaches \( 2\pi r \) (circumference), not \( 2\pi \) (lacks radius). Incorrect.
• Option C: As \( n \) increases, the polygon’s area gets closer to the circle’s area. Correct.
• Option D: The perimeter (\( sn \)) approaches the circle’s circumference (\( 2\pi r \)). Correct.
• Option E: As \( n \) increases, \( h \) approaches the radius \( r \). Correct.

Answer:

C. The area of the polygon approaches the area of the circle.
D. The perimeter of the polygon approaches the circumference of the circle.
E. The height of the triangle approaches the length of the radius of the circle.