Answer:
Here's what I get
Step-by-step explanation:
a. Net of a cube
Fig. 1 is the net of a cube
b. Does the formula work?
Tony's formula works if you ignore dimensions.
There are six squares in the net of a cube.
If each side has a unit length s, the total area of the cube is 6s.
c. Will the formula work for any rectangular prism?
No, because a rectangular prism has sides of three different lengths — l, w, and h — as in Fig. 2.
d. Area of a rectangular prism
A rectangular prism has six faces.
A top (T) and a bottom (b) — A = 2×l×w
A left (L) and a right (R) — A = 2×l×h
A front (F) and a back (B) — A = 2×w×h
Total area = 2lw + 2lh + 2wh
If l = 5 m, w = 6 m and h = 8 m,
![\begin{array}{rl}A &=& \text{2$\times$ 5 m $\times$ 6 m + 2$\times$ 5 m $\times$ 8 m + 2 $\times$ 6 m $\times$ 8 m}\\&=& \text{60 m}^{2} + \text{80 m}^{2} + \text{96 m}^{2}\\&=& \textbf{236 m}^{2}\\\end{array}](https://tex.z-dn.net/?f=%5Cbegin%7Barray%7D%7Brl%7DA%20%26%3D%26%20%5Ctext%7B2%24%5Ctimes%24%205%20m%20%24%5Ctimes%24%206%20m%20%2B%202%24%5Ctimes%24%205%20m%20%24%5Ctimes%24%208%20m%20%2B%202%20%24%5Ctimes%24%206%20m%20%24%5Ctimes%24%208%20m%7D%5C%5C%26%3D%26%20%5Ctext%7B60%20m%7D%5E%7B2%7D%20%2B%20%5Ctext%7B80%20m%7D%5E%7B2%7D%20%2B%20%5Ctext%7B96%20m%7D%5E%7B2%7D%5C%5C%26%3D%26%20%5Ctextbf%7B236%20m%7D%5E%7B2%7D%5C%5C%5Cend%7Barray%7D)