The area of the regular triangular prism is given by the formula:
[tex]A=s(\frac{\sqrt{3}}{2}s+3h)[/tex]
Where:
s = side of the triangle = 4root(3)
h = the height = 9
Substitute the values:
[tex]A=4\sqrt{3}(\frac{\sqrt{3}}{2}\times4\sqrt{3}+3\times9)[/tex]
Simplify:
[tex]\begin{gathered} A=4\sqrt{3}(\frac{3\times4}{2}+27)=4\sqrt{3}(\frac{12}{2}+27)=4\sqrt{3}(6+27)=4\sqrt{3}(33) \\ A=228.6\approx229\text{ units}^2 \end{gathered}[/tex]
Answer: 229 units²
