Challenge Problems for 22-4 n a
Challenge Problems for 22-4 1. Find a formula for the area of a regular polygon in terms of n, the number of sides, and s, the side 1 length. In other words, in the formula = ∙ ∙ , get rid of the apothem a and replace it with an 2 equivalent trig expression involving n and s. Then simplify your answer. a r s 2. Use the formula from Q1 to find the exact area of a hexagon with a side length of 10 inches. 3. A machine part is in the shape of a half-circle with a radius of 10 inches. Small holes are drilled as shown in the figure. Find the coordinates of each hole. 4. Obey the Law: You can use right triangle trigonometry on non-right triangles if you use an altitude. a) Write an equation for ℎ using ∠ and side . F b) Write an equation for ℎ using ∠ and side . d e h D E c) Substitute your expression for ℎ from part a) into ℎ in the equation from part b). Finally, divide both sides of your new equation by .