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 formula for the area of a triangle is $A=\frac{1}{2}bh$. Here, $b = 12$ m and $h = 8$ m. So, $A_{base}=\frac{1}{2}\times12\times8=48$ m². Since there are 2 triangular bases, the total area of the bases is $2\times48 = 96$ m².

Step2: Calculate area of first rectangular face

The first rectangular face has dimensions 15 m (length) and 8 m (width). So, $A_1=15\times8 = 120$ m².

Step3: Calculate area of second rectangular face

The second rectangular face has dimensions 15 m (length) and 12 m (width). So, $A_2=15\times12 = 180$ m².

Step4: Calculate area of third rectangular face

The third rectangular face has dimensions 15 m (length) and 13 m (width). So, $A_3=15\times13 = 195$ m².

Step5: Calculate total surface area

The total surface area $A_{total}=A_{bases}+A_1 + A_2+A_3=96 + 120+180 + 195=591$ m².

Answer:

591 m²