Could someone please check my work!

5x^2 + 5y^2 = 28 - 2x^2 - 2y^2

7x^2 + 7y^2 = 28

y = +/- sqrt(4-x^2) . . . z = 20

z = 5x^2 + 5y^2

f_x = 10x = 10*r*cos(theta)

f_y = 10y = 10*r*sin(theta)

z = 28 - 2x^2 - 2y^2

f_x = -4x = -4*r*cos(theta)

f_y = -4y = -4*r*sin(theta)

SA = int(int_R(sqrt(f_(x)^2 = f_(y)^2 + 1)dA

int(int(sqrt(16r^2*cos^2(theta) + 16r^2*sin^2(theta) + 1)r dr d(theta)..

Note the limits of integration are, respectively, 0 to 2Pi, 0 to 2..

I did it out and got 172.6 ...

PLEASE would someone help me determine if this is right.

For the avg. distance I'm not sure.