Question

What is the area of a regular decagon with a radius of 8 centimeters?

Answer 1

did you get this yet?

Answer 2

No, I can't find a formula that I understand.

Answer 3

do you know trig or are you using something else?

Answer 4

Do not know trig! Trying my hardest, I have difficulties with even simple math.

Answer 5

i am not sure i can do it without trig. maybe Anwar?

Answer 6

oops he just left.

Answer 7

:/ Can you explain it to me? If you can explain the formula, I can do that.

Answer 8

ok you need to think of splitting it up in to right triangles. you will have twenty of them.

Answer 9

wait i have a better idea, because i see this one involves trig as well. so we might as well do this. the formula for the area of a triangle is \[\frac{1}{2}bcsin(A)\] where A is the angle between the sides. in this case the sides are both of length 8 and the angle is 360/10=36

Answer 10

so unless i miss my guess each of these 10 triangles (not 20, just ten) has area \[32sin(36)=18.809\]

Answer 11

multiply by 10 to get the total area. now i am going to check to see if this is correct. but i cannot see a way to do it without using some trig.

Answer 12

Thank you for trying so hard, though, and this I can understand fairly easy.

Answer 13

welcome, but don't quote me!

Answer 14

yea but i think i am wrong. i will keep trying.

Answer 15

ok let me try again. is this for a trig class?

Answer 16

in any case break this thing up into 20 right triangles, each with hypotenuse 8.
the small angle between the long sides of those triangle is 18 degrees because it is 360/20

Answer 17

call the long side of those triangles b
\[cos(18)=\frac{b}{10}\] so the long side is
\[b=10cos(18)=9.51\] rounded. the last side we find by pythagoras since we know the hypotenuse and the long side. the short side is
\[\sqrt{10^2-9.51^2}=3.09\] rounded.

Answer 18

the area of each of those twenty triangles is therefore \[\frac{1}{2} 9.21 \times3.09\]

Answer 19

since there are twenty of them just compute \[10\times 9.21 \times 3.09\]

Answer 20

i know this answer is correct (i mean i know the area is) because i did checked it here:
http://www.cleavebooks.co.uk/scol/calpolyg.htm

Answer 21

i see that i used 10 instead of 8. you should use 8. but i also got the same answer using the sine method so forget it.