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.**

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