Question

Question 3 (4 points)Using the Triangular Prism in the picture, find the Lateral Area, the Area of a Single Base,and the TOTAL Surface Area:?? in9 in-16 in12 inFirst find the missing length =in

Answer 1

Given the triangular prism;

Using the Pythagorean Theorem;

`\begin{gathered} h=√(o^2+a^2) \\ \\ Where\text{ }h=hypotenuse,o=opposie,a=adjacent \end{gathered}`

Thus;

`\begin{gathered} h=√(9^2+12^2) \\ \\ h=√(225) \\ \\ h=15in \end{gathered}`

Thus, the missing length is 15 in.

Also, the lateral area, L, is;

`\begin{gathered} L=(h+o+a)H \\ \\ \text{ Where }H=height\text{ } \\ \\ L=(15+12+9)(16) \\ \\ L=576in^2 \end{gathered}`

ANSWER:

`Lateral\text{ }Area=576in^2`

Also, the single base area, B, is;

`\begin{gathered} B=(1)/(2)oa \\ \\ B=(1)/(2)(9)(12) \\ \\ B=54in^2 \\ \end{gathered}`

ANSWER:

`Single\text{ }Base\text{ }Area=54in^2`

Then, the surface area, S, is;

`\begin{gathered} S=L+2B \\ \\ S=576+2(54) \\ \\ S=684in^2 \end{gathered}`

ANSWER:

`Surface\text{ }Area=684in^2`