Question

What is the volume of a regular octagonal based prism with a height of 20 cm and base side lengths of 6cm?
BEST ANSWER GETS MEDAL!!

Answer 1

do you know how to find the area of the octagon base?

Answer 2

I don't remember

Answer 3

do any of these formulas look familiar (see the link)

http://www.mathwords.com/a/area_regular_polygon.htm

Answer 4

I don't know the apothem method, it doesn't look familiar to me

Answer 5

it turns out that the area of any regular polygon (all sides have to be equal; all angles have to be equal) is this

\[\Large A = \frac{1}{4}*n*s^2*\cot\left(\frac{180}{n}\right)\]

n = number of sides
s = length of each side

Answer 6

what is cot?

Answer 7

cot stands for cotangent

Answer 8

I don't know how to do that

Answer 9

it is one of the 6 trig ratios you'll learn in trigonometry class

Answer 10

for now we can use a calculator to make things easier

Answer 11

i learned sin, tan, and cos

Answer 12

cotangent = 1/(tangent)

Answer 13

example:

cot(5) = 1/tan(5)

Answer 14

oh okay cool

Answer 15

now what?

Answer 16

In this case, n = 8 and s = 6, so...
\[\Large A = \frac{1}{4}*n*s^2*\cot\left(\frac{180}{n}\right)\]
\[\Large A = \frac{1}{4}*8*6^2*\cot\left(\frac{180}{8}\right)\]
\[\Large A \approx 173.8233764908496681\]


for the last step, I used this calculator
http://web2.0calc.com/
see the attached image


So the approximate area of the octagon is roughly 173.8233764908496681 square centimeters

Answer 17

Finding the area of the octagon is the hardest step. After that it gets easier.

To find the volume of the prism, you multiply the area of the base by the height of the prism

Volume = (area of base) * (height of prism)

Answer 18

let me know if this makes sense or not

Answer 19

It makes sense but i haven't learned any of this stuff yet, so i get how it would make sense but i need to show my knowledge of what was learned in class

Answer 20

let's try another method

what you can do is cut the octagon into 8 congruent triangles

so let's start off with an octagon

Answer 21

Okay cool

Answer 22

now let's divide it up into 8 triangles

Answer 23

let's focus on just one triangle (the other triangles will be congruent so we don't need to focus on all 8 at the same time)

Answer 24

the side length of the octagon is 6, so the base of the triangle is 6

Answer 25

we can cut that distance in half to get 3