What is the surface area of this triangular prism?
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The surface area of this prism is ##36 in^2##. Even though the explanation might seem slightly long it is really easily broken down into pieces so I highly recommend you read and learn from it. 
In extremely simple terms imagine you have a woodblock shaped like the triangular prism in picture you attached.
The surface area of that prism is basically all the areas that you can touch (total area of the outside/surface).
Let’s calculate each side separately and then we can add them up at the end.
The triangular sides:
This triangular surface is 3 inches (height) by 4 inches (base). Using the area formula for triangles (##1/2bh## where ##b## is the base and ##h## is the height) the area of the triangular surface is ##1/2bh=1/2(3 in)(4 in) = 1/2 (12 in^2)=6 in^2##.
There are two triangular surfaces (one in yellow and white) so multiply the area of the triangle by factor of ##2##: ##6 in^2 times 2 = color(blue)(12 in^2)##
The bottom of the prism:
The bottom of the prism is a rectangle since the angles are 90 degrees. The formula to calculate the area of the triangle is ##length times width## and the rectangle at the bottom has base of ##4 in## and width of ##2 in##. Therefore ##length times width = 4 in times 2 in = color(orange)(8 in^2)##
The wall of the prism:
This side of the prism (outlined in pink) is also a rectangle with a width of ##3 in## and length of ##2 in## (since the blue-circled sides are parallel and the prism structure is perpendicular).
Therefore ##length times width = 2 in times 3 in = color(pink)(6 in^2)##
The slanted side:
This side is also a rectangle with length of ##5 in## and a width of ##2 in##. Therefore ##length times width = 5 in times 2 in = color(green)(10 in^2)##
To find the surface area add all the areas up:
##color(blue)(12 in^2) + color(orange)(8 in^2) + color(pink)(6 in^2) + color(green)(10 in^2) = 36 in^2##
If you have any questions please do not hesitate to leave a comment!
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