## Regular Polygons with Rational Area or Perimeter.

Write an expression that finds the area of one triangle in an n-gon, using a to represent the apothem and s to represent a side of the n-gon. Then use the expression to write a formula that finds the area of the entire n-gon, where n represents the number of sides of the n-gon. Explain how to determine the perimeter of a polygon, P.

Question 194497This question is from textbook: Write the perimeter formula of a rectangle, and then substitute the following conditions into the formula: The perimeter of a rectangular garden is 100 feet, and the length of the garden in 12 feet more than the width. Use x to represent the width. This question is from textbook Answer by doukungfoo(195) (Show Source).

Formula for the area of a regular polygon. 2. Given the radius (circumradius) If you know the radius (distance from the center to a vertex, see figure above): where r is the radius (circumradius) n is the number of sides sin is the sine function calculated in degrees (see Trigonometry Overview). To see how this equation is derived, see Derivation of regular polygon area formula.

Start studying Chapter 7 - Perimeter, Circumference, Area. Learn vocabulary, terms, and more with flashcards, games, and other study tools.

Given the radius r. The radius of a regular polygon is the distance from the center to any vertex. In the figure below the leg of the isosceles triangle is a radius r of the polygon. We add a perpendicular h from the apex to the base. In this case, let t be the whole angle at the apex. From the figure we see that The area of any triangle is half the base times height, and since x is already.

Another interesting thought suggested by Ferry’s puzzle is to give the exact formula for the expected area of an n-sided convex polygon whose vertices are randomly selected points on the unit circle (assuming a uniform distribution on the perimeter). To answer this question we obviously can't make use of the small-angle assumption, so we must use the full sine formulas.

Students will deduce the general expressions for perimeter and area of an n-sided polygon based on the previous lessons. Students will understand the concept of representing the number of sides of a regular polygon with the variable n. Procedure: Perimeter. 1. Collectively recall the various expressions discovered from the previous lessons.