screen sizes (TVs, computers) are given by measuring the length of the diagonal. If the base length of a 40-inch TV is 32", what is the surface area of the TV screen?

The base length, the screen height and the screen diagonal form a right-angle triangle.

Therefore, you can use pythagorean theorem to calculate screen height:
sqrt(40**2 - 32**2) = 24.0
Then surface is length by height:
32 * 24 = 768