Question

The area of a given hexagon is equal to the area of an equilateral triangle whose perimeter is 36 inches. Find the length of a side of the regular hexagon.

Answer 1

an equilateral triangle has 3 equal sides so than the perimeter is 36 inches so this mean that a side has a length of 12 inches
so than you know that the length of a side of an equilateral triangle is equal 12 so can yo calculi arae of this triangle equal how many ?

Answer 2

sorry - can you calculi area of this triangle ?

Answer 3

base x height?

Answer 4

no

area of a triangle is base time height divide 2

Answer 5

but in this case first you need calculi the length of this height - yes ?

Answer 6

yes?

Answer 7

any idea to how you can calculi the length of this height ?

Answer 8

you can using pythagora"s theorem or the sin of 60 degree - what you like using ?

Answer 9

or tan or cot ,what you like using

Answer 10

pyth

Answer 11

do you know
exactly this i wan writing now

Answer 12

so what say pyth in this case ?

Answer 13

height so h^2 = ?

Answer 14

you dont know it ?

Answer 15

h^2 = 12^2 -6^2 yes ?

Answer 16

yes

Answer 17

so than h = ?

Answer 18

idk

Answer 19

h = sqrt(144-36) = ?

Answer 20

108

Answer 21

yes but sqrt108 = ?

Answer 22

If you like to try a different approach, here are some hints:

Answer 23

Oops, the bottom line should read
S^2/A=s^2/a
s^2=S^2(a/A)
s^2=S^2(1/6)
s=S*sqrt(1/6)=S/sqrt(6)