Answer
The lateral area of the prism is 900 in squared
The surface area of the prism is 960 in squared
Explanation
Given:
The first side of the triangular base, a = 12 in
The second side of the triangular base, b = 13 in
The height of the prism, h = 30 in
What to find:
The lateral area and surface area of the prism.
Step-by-step solution:
The first step is to find the third side, c of the triangular base using Pythagoras rule.
[tex]\begin{gathered} b^2=c^2+a^2 \\ \\ 13^2=c^2+12^2 \\ \\ c^2=13^2-12^2 \\ \\ c^2=169-144 \\ \\ c^2=25 \\ \\ c=\sqrt{25} \\ \\ c=5\text{ }in \end{gathered}[/tex]
Now, the next step is to calculate the lateral area of the prism using the formula below.
[tex]\begin{gathered} L.A=ha+hb+hc \\ \\ L.A=30\times12+30\times13+30\times5 \\ \\ L.A=360+390+150 \\ \\ L.A=900\text{ }in^2 \end{gathered}[/tex]
The lateral area of the prism is 900 in squared
The final step is to calculate the surface area of the prism using the formula below.
[tex]S.A=Lateral\text{ }Area+Base\text{ }Area[/tex]
The base area is
[tex]=2(\frac{1}{2}cb)=2(\frac{1}{2}\times5\times12)=2(\frac{60}{2})=60\text{ }in^2[/tex]
Therefore, the Surface Area = (900 + 60) = 960 in squared
