Phil is making a number cube out of cardboard He traces one face of the number cube onto a coordinate grid The coordinates of two opposite vertices of the face are (4, 8) and (12, 16) What is the surface area, in square units, of Phil's entire number cube?

Explanation:

Let A = (4,8) and B = (12,16)

Form point C at the location (12,8). Note how points A and C are on the same horizontal level, or they have the same y coordinate.

The distance from A(4,8) to C(12,8) is 12-4 = 8 units. Ignore the y coordinates and subtract the x coordinates. This trick only works for horizontal line segments.

So we can see that each square face has a side length of 8 units. The area of each square face is 8^2 = 8*8 = 64 square units.

There are six of these faces, so 6*64 = 384 square units is the total surface area of the number cube.