Answer:
The diagonal of the given regular solid is [tex]2\sqrt{21}\ or\ 9.165[/tex]
Step-by-step explanation:
Given:
The given regular solid is a cuboid or a rectangular prism.
Length of the cuboid is, [tex]l=8[/tex]
Width of the cuboid is, [tex]w=4[/tex]
Height of the cuboid is, [tex]h=2[/tex]
We know that, for a cuboid of length 'l', width 'w' and height 'h', the diagonal length 'd' is given as:
[tex]d=\sqrt{l^2+w^2+h^2}[/tex]
Plug in 8 for 'l', 4 for 'w', 2 for 'h' and solve for 'd'. This gives,
[tex]d=\sqrt{8^2+4^2+2^2}\\\\d=\sqrt{64+16+4}\\\\d=\sqrt{84}\\\\d=\sqrt{4\times 21}\\\\d=2\sqrt{21}\ or\ 9.165[/tex]
Therefore, the diagonal of the given regular solid is [tex]2\sqrt{21}\ or\ 9.165[/tex]
