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 area formula for a triangle is $A=\frac{1}{2}bh$. Here, $b = 12$ m and $h=5$ m. So, $A_{triangle}=\frac{1}{2}\times12\times5= 30$ m². Since there are 2 triangular bases, the total area of the bases is $2\times30 = 60$ m².

Step2: Calculate area of first rectangular face

One rectangular face has dimensions 9 m (height of the prism) and 12 m. So its area $A_{1}=9\times12 = 108$ m².

Step3: Calculate area of second rectangular face

Another rectangular face has dimensions 9 m and 5 m. So its area $A_{2}=9\times5=45$ m².

Step4: Calculate area of third rectangular face

The third rectangular face has dimensions 9 m and 13 m. So its area $A_{3}=9\times13 = 117$ m².

Step5: Calculate total surface area

The total surface area $A_{total}$ of the triangular - prism is the sum of the areas of the bases and the rectangular faces. So $A_{total}=60 + 108+45 + 117=330$ m².

Answer:

330 m²