Question

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

Explanation:

Step1: Calculate area of triangular bases

The base of the triangle is $5$m and height is $12$m. Area of a triangle $A_{triangle}=\frac{1}{2}\times base\times height$. So $A_{triangle}=\frac{1}{2}\times5\times12 = 30$ $m^{2}$. Since there are 2 triangular bases, total area of bases $A_{bases}=2\times30=60$ $m^{2}$.

Step2: Calculate area of first rectangular face

One rectangular face has dimensions $7$m (length) and $12$m (width). Area $A_{1}=7\times12 = 84$ $m^{2}$.

Step3: Calculate area of second rectangular face

Another rectangular face has dimensions $7$m (length) and $5$m (width). Area $A_{2}=7\times5 = 35$ $m^{2}$.

Step4: Calculate area of third rectangular face

The third rectangular face has dimensions $7$m (length) and $13$m (width). Area $A_{3}=7\times13 = 91$ $m^{2}$.

Step5: Calculate total surface area

Total surface area $A = A_{bases}+A_{1}+A_{2}+A_{3}=60 + 84+35 + 91=270$ $m^{2}$.

Answer:

$270$ $m^{2}$