find the surface area of this triangular prism. be sure to include the correct unit in your answer.

Explanation:

Step1: Calculate area of triangular faces

The area of a triangle is $A=\frac{1}{2}bh$. For the triangular faces with base $b = 5$ in and height $h=12$ in, $A_{triangle}=\frac{1}{2}\times5\times12 = 30$ in². Since there are 2 triangular faces, the total area of triangular faces is $2\times30=60$ in².

Step2: Calculate area of first rectangular face

One rectangular face has dimensions 5 in (width) and 13 in (length). Its area $A_{rect1}=5\times13 = 65$ in².

Step3: Calculate area of second rectangular face

Another rectangular face has dimensions 12 in (width) and 13 in (length). Its area $A_{rect2}=12\times13 = 156$ in².

Step4: Calculate area of third rectangular face

The third - rectangular face has dimensions 13 in (length) and 13 in (width). Its area $A_{rect3}=13\times13 = 169$ in².

Step5: Calculate total surface area

The total surface area $A = A_{triangles}+A_{rect1}+A_{rect2}+A_{rect3}=60 + 65+156+169=450$ in².

Answer:

450 in²