Answer:
[tex]150\sqrt{59}[/tex]
Step-by-step explanation:
[tex]z = 3x + 7y\\\\\frac{dz}{dx} = 3\:\:\: and \:\:\: \frac{dz}{dy} =7[/tex]
[tex]Area = \int\limits^5_0 \int\limits^{30}_0 \sqrt{1 + (\frac{dz}{dx})^2+ (\frac{dz}{dy})^2}\:dx\:dy\\\\Area = \int\limits^5_0 \int\limits^{30}_0 \sqrt{1 + 9+ 49}\:dx\:dy=\sqrt{59}*30*5=150\sqrt{59}[/tex]
