Question

2.) find the surface area of the triangular prism below. show all work! 14 in 10 in 8 in 12 in 10 in

Explanation:

Step1: Find area of triangular bases

The area formula for a triangle is $A=\frac{1}{2}bh$. Here, $b = 8$ in and $h=12$ in. So, $A_{base}=\frac{1}{2}\times8\times12=48$ in². Since there are 2 triangular bases, the total area of the bases is $2\times48 = 96$ in².

Step2: Find area of rectangular faces

There are 3 rectangular faces.
Face 1: Dimensions 10 in and 14 in, area $A_1=10\times14 = 140$ in².
Face 2: Dimensions 10 in and 12 in, area $A_2=10\times12=120$ in².
Face 3: Dimensions 10 in and 8 in, area $A_3=10\times8 = 80$ in².
The total area of the rectangular faces is $A_{rect}=140 + 120+80=340$ in².

Step3: Calculate total surface area

The total surface area $A$ of the triangular - prism is the sum of the area of the bases and the area of the rectangular faces. So, $A=96 + 340=436$ in².

Answer:

436 in²