19. If a regular hexagon has sides equal to 12, what is the area? (this problem comes up over and over again in different ways. make sure you can work it!)
Answer: 62.4 sq. units. You can find this using the formula for the area of a regular polygon, (1/2 x apothem x perimeter). You can also find the area of one equilateral triangle with side 12, and multiplying that by 6.20. Given a pentagonal prism.
a. How many total vertices? 10
b. How many lateral faces? 5
c. How many total faces? 7
d. How many bases? 2
F+V=e+2 Total Faces + Vertices = edges + 2
21. Find the area of an equilateral triangle with perimeter 18.
If perimeter is 18, then each side is 6. Area: 15.6 sq. units
22. If a circle has diameter 20, find: (so radius is 10)
a. area of the circle 100 pi or 314.2 sq. units
b. circumference of the circle 62.8
c. volume of a sphere with the same diameter 4188.8 cu. un.
d. area of a sphere with the same diameter 1256.5 sq.un.
e. area of semi-circle 50 pi sq. un. or 157.1 sq. un.