Ok... to find the total surface area we have to realize a couple of things. First it's a triangular prism so we are dealing with 5 sides. Also the triangular sides are going to be congruent so all the side Lengths will also be congruent. The rectangular sides of the prism will have congruence as well. Lastly we have to know that to find the total surface area, you have to find the area of each side and add them together....
First the triangles. The area formula for a triangle is a = 1/2 base × height.
Since they are right triangles, the base and height are the legs of the right angle, so...
a = 1/2 (8 × 15)
a = 4 × 15 = 60 in^2
Don't forget we have 2 of them so surface area of both is 120 in^2.
Now the rectangles...
a = base × height
1) a= 13 × 8 = 104 in^2
2) a = 15 × 13 = 195 in^2
3) a = 13 × 17 = 221 in ^2
Now add them all up...
104 + 195 + 221 + 120 =
640 in^2 total surface area
