Find the surface area of this triangular prism. Hint: you can draw the net of the shape to help you.
So we have- that this is a triangular prism. The bases, the parallel faces, are triangles. And it’s a prism because the rest of the faces or the sides is what we can call them are rectangles. That’s what makes up a prism: the two bases and then the rest are rectangles. So if we would like the surface area of this shape, we need to add the area of all of the faces together. So our hint tells us to draw the net of this shape, which would be all of the faces laying flat so we can easily see them. So let’s go ahead and do that.
So we have these two triangles, which are our bases; we have the pink rectangle, found back here; and we have this length as 15, because it matches this one. We have the bottom rectangle, and keep in mind that these are not to scale, and then lastly the blue rectangle. So here we’ve drawn the net of the shape. So if we find the area of each of these shapes and we add them together, we will have the surface area. The area of a triangle is one-half times the base times the height. So for the two rectangles, we have one-half times their base of eight times their perpendicular height, which is six. And it’s important that we know that that’s a right angle in the corner of the triangle, because that let’s us know that the six is indeed perpendicular.
So we won’t be using the 10. So we can either take that and multiply by two or write it twice since we have two triangles. Now we have the rectangles, and the area of a rectangle is length times width. So we need to take six times 15 for the pink rectangle, eight times 15 for the green rectangle, and 10 times 15 for the blue rectangle. So let’s begin to simplify. One-half times eight times six, well one-half times eight is four, and four times six is 24. So we’ll repeat that process again for the second triangle. And then we have six times 15, which is 90, and then eight times 15, which is 120, and then 10 times 15, which is 150. Adding these numbers together, we get 408. Now we don’t have any units for this shape, so we could say that it’s an area of 408 square units because an area should be squared. And this will be our final answer.