Question

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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, $b = 6$ in and $h = 8$ in. So, $A_{triangle}=\frac{1}{2}\times6\times8= 24$ in². Since there are 2 triangular bases, the total area of the bases is $2\times24 = 48$ in².

Step2: Calculate area of rectangular faces

There are 3 rectangular faces.
Face 1: with dimensions 6 in and 7 in, $A_1=6\times7 = 42$ in².
Face 2: with dimensions 8 in and 7 in, $A_2=8\times7=56$ in².
Face 3: with dimensions 10 in and 7 in, $A_3 = 10\times7=70$ in².
The total area of the rectangular faces is $A_{rectangles}=42 + 56+70=168$ in².

Step3: Calculate total surface area

The surface - area of the triangular prism is the sum of the area of the bases and the area of the rectangular faces. So, $A = 48+168=216$ in².

Answer:

216 in²