1. The Pythagorean Theorem can be used to find distances between two points on a grid. But what about finding distances in three-dimensional space? Consider a rectangular box, which has length l, width w, and height h. What is the distance from one corner to the opposite corner in terms of l, w, and h?

Question

2. Find an example of an equilateral hexagon whose sides are all square root of 13 units long. Give coordinates for all six points. [Hint: Think carefully about where to draw the hexagon on a coordinate grid.]

If someone could please give me an explanation, I'd be very grateful. I have no idea how to solve number 1, and I feel like I'm over thinking number 2.

Answer 1

actually the Pythagorean theorem is only used to find the length of a missing side of a right triangle, you use the distance formula which is
square root (x-x)^2+(y-y)^2

Answer 2

What if this is a three dimensional rectangle? The corners could be two corners in different regions.

Answer 3

For example, what if I had to measure the front bottom left corner to the rear top right corner?