Solution:
Given the triangular prism;
Using the Pythagorean Theorem;
[tex]\begin{gathered} h=\sqrt{o^2+a^2} \\ \\ Where\text{ }h=hypotenuse,o=opposie,a=adjacent \end{gathered}[/tex]
Thus;
[tex]\begin{gathered} h=\sqrt{9^2+12^2} \\ \\ h=\sqrt{225} \\ \\ h=15in \end{gathered}[/tex]
Thus, the missing length is 15 in.
Also, the lateral area, L, is;
[tex]\begin{gathered} L=(h+o+a)H \\ \\ \text{ Where }H=height\text{ } \\ \\ L=(15+12+9)(16) \\ \\ L=576in^2 \end{gathered}[/tex]
ANSWER:
[tex]Lateral\text{ }Area=576in^2[/tex]
Also, the single base area, B, is;
[tex]\begin{gathered} B=\frac{1}{2}oa \\ \\ B=\frac{1}{2}(9)(12) \\ \\ B=54in^2 \\ \end{gathered}[/tex]
ANSWER:
[tex]Single\text{ }Base\text{ }Area=54in^2[/tex]
Then, the surface area, S, is;
[tex]\begin{gathered} S=L+2B \\ \\ S=576+2(54) \\ \\ S=684in^2 \end{gathered}[/tex]
ANSWER:
[tex]Surface\text{ }Area=684in^2[/tex]
