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 𝐴 = 𝑎 ∙ 𝑛 ∙ 𝑠, 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 ∠𝐷 and side 𝑒.
F
b) Write an equation for ℎ using ∠𝐸 and side 𝑑.
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 𝑒𝑑.