Applied problem of multivariable calculus with integrals. How to solve this problem:

A medal has the shape of the portion of the plane $x + z = 1$ lying inside the cylinder $$x^2 + \frac{y^2}{2} = 1.$$ The edge of the medal is covered in gold and it costs $\$ 20$ per linear inch, while the medal's surface is covered in silver and it costs $\$10$ per square inch. How much does each medal cost? 

The units for the variables are not stated explicitly.



I think this problem is solved with a couple of integrals, but really have no clue on how to set them up.
I think I found the cost of the edge 

Find the angle the plane slices through the cylinder using the dot product of the normal vectors of the plane and the cylinder

n1(plane>=&lt;1,0,1>

n2(cyl)=&lt;0,1,0>

n1*n2=||n1||||n2||cos(theta)

Theta =45

Then use the formula for the circumferance of a cylinder 

C=2*pi*sqrt((a^2+b^2)/2)

and make a right triangle with the angle theta to find the circumference of the slice

no idea about the area of the coin good luck hope this helps
I think I found the cost of the edge 

Find the angle the plane slices through the cylinder using the dot product of the normal vectors of the plane and the cylinder

n1(plane>=&lt;1,0,1>

n2(cyl)=&lt;0,1,0>

n1*n2=||n1||||n2||cos(theta)

Theta =45

Then use the formula for the circumferance of a cylinder 

C=2*pi*sqrt((a^2+b^2)/2)

and make a right triangle with the angle theta to find the circumference of the slice

no idea about the area of the coin good luck hope this helps