Problem of the Week 20

Suppose one vertex angle of a regular octagon is trisected as shown in the figure.  Each side of the octagon measures 4 units.  Find the area of the shaded region.



Alternate Problem 20

Suppose it takes 3.25 miles along a highway to go from an altitude of 5000 feet to an altitude of 6000 feet.  What is the percent grade?*

*The grade of a highway is the vertical rise in distance divided by the change in horizontal distance for the rise.


Extension Problem 20

Suppose n is a prime number and n1, n2, n3, and n4 are primes that are defined as follows.





What is the least possible value of n which gives distinct prime values for the other variables?