Question

Calculus finding maximum area. Twenty feet of wire is to be used to create two figures. How much wire should be used for each figure so that the total area is a maximum. Figures are a square and a regular pentagon

Answer 1

A=s^2+1/48(√5∗(5+2(√5)))x^2

20 = 4s + 5x

solve for x or s
plug it into the the equation above then differentiate

set the differentiated equation equal to 0 to find critical values
use the 2nd derivative test to determine if your critical point is a maximum
if its a minimum test your end points as the question is hard bounded
0≤x≤20

Answer 2

Awesome, but how did you come up with that area formula?

Answer 3

That area formula messed up when i typed it in... let me rewrite it.

Answer 4

\[A = s^2 + 1/4(\sqrt{5(5+2\sqrt{5}}*x^2)\]

Answer 5

I had the area of a regular pentagon on my calculator. To form the total Area formula to be maximized you just add the area of the square to the area of the regular polygon and set it equal to some value i picked A.

Answer 6

in this case the polygon was a pentagon

Answer 7

So that is the formula for the square and the pentagon added together correct. The geometry is what is messing me up