Let's work out the surface area of this triangular prism. The key to working out the surface area of a prism, of any shape, is realizing that you just need to find the areas of each face. Here, we have 3 distinct shapes of faces. We have this triangle here, we have this rectangle on the side, and we also have a rectangle on the base. We noticed that there are 2 of these triangular and 2 of these rectangular side faces. So, if you work out the area of them once, we just multiply that by 2 and that will give us the surface area we need. So, let's label those faces. 1, 2, and the bottom is 3. We also need some dimensions. So, let's say we have a height here of 4, we have a base here of 2.these are all centimeters, let's make sure we have our units in there. We have a diagonal length here of 3 centimeters. And finally, a length of 4 centimeters. That is all the information we need. First of all, let's work out the area of the surface 1. The area of 1, is one half multiplied by 2 times 4. 8 multiplied by a half is 4 centimeters squared. That's because the area of a triangle is one half times base times height. The area of 2 is 3 multiplied by 4 because it's a rectangle, which is 15 centimeters squared. Finally, the area of 3, this base here is 4 multiplied by the base of the triangle, which is 2, which is 10 centimeters squared. What we do now is we add these two together, 15 and 4, to give us 19. so, that's the area of 1 and 2.19 centimeters squared. And we know that if we multiplied this by 2, because there are 2 of each face, we get the surface area of all that combined. So, this gives us 38 centimeters squared. Then we add on the base, which is 10 centimeters squared, and this gives us the final total surface area, which is equal to 48 centimeters squared. Just to recap, the first thing we do is we work out the separate surface area of each surface. So, we have 1, 2, and 3. We work out the area for 1 here: half times base times height. We work out the area of 2 by multiplying 3 and 5. We work out the area of 3 by multiplying 2 by 5. We then add the first two together because there are 2 of those surfaces on the prism. Multiply this by 2, that gives us the total surface area for those 4 faces. We then add the surface area of the face, 10 centimeters squared, and this gives us the final total surface area of the prism. And that's how to work out the surface area of a triangular prism. .

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