Question

written response
as shown in the figure below, ( f = )______.
upload a picture or video, no more than 10 pictures or 800m for the video

Explanation:

Step1: Find the diagonal of the base

The base is a rectangle with length \(l = 5\) and width \(w=4\). Using the Pythagorean theorem \(d_{base}^2=5^{2}+4^{2}\).

$$d_{base}^2 = 25 + 16=41$$

Step2: Find the space - diagonal \(t\)

The height of the cuboid \(h = 6\). Using the three - dimensional Pythagorean theorem \(t^{2}=d_{base}^2+h^{2}\). Substitute \(d_{base}^2 = 41\) and \(h = 6\) (so \(h^{2}=36\)) into the formula:

$$t^{2}=41 + 36$$

$$t^{2}=77$$

$$t=\sqrt{77}$$

Answer:

\(\sqrt{77}\)