Areas of Polygons Review

avaeliza · 2019-03-24 01:17:10

Hello! I have a lesson review that I need some help figuring out. I'll post 3-7 and then the next set if I still need help. Thanks

For #1-7, calculate the area for each of the polygons described below. Round answers to the nearest hundredth and remember to include the unit of measure.

Stuck on #3 right now. Here's what I have so far:
#3. A regular pentagon with a side of 3 centimeters
2 x side angle + central angle = 180
2 x side angle + 72 = 180
2 x 54 + 72 = 180
tan(54) ?????????

I followed my teacher's example of a nonagon here:
Find the measure of one base angle.
central angle = 360/9 = 40
2 * side angle + central angle = 180
2 * side angle + 40 = 180
2 * side angle = 140
side angle = 70°

Use a trig ratio to find the height of one triangle.
tan(70°) = h/(8/2)
h = 4*tan(70°)
h = 10.99 in

I can't figure out what the h/8/2 part means.

I haven't tried 4-7 yet because I think I might run into the same issues.

#4. A regular hexagon with a side of 10 cm

#5. A regular heptagon with a side of 7 inches.

#6. A trapezoid where the height is 18 cm, base 1 = 16 cm and b2 = 8 cm.

#7. A trapezoid where the height = 7 mm, base 1 = 26 mm and base 2 = 9 mm.