How to Find the Surface Area of a Triangular Prism Math with Mr J

Welcome to Math with Mr. In this video, I'm going to cover how to find the surface area of triangular prism. And remember, the surface area, simply put, is the area of the outside part or layer of 3D figure. And when it comes to triangular prisms, they have five faces. So, we need to find the area of each of those five faces, add them together, and we'll get the surface area. So, at the top of your screen where it says SA right here, that means surface area. So, this is how we're going to organize our problem and add up the areas of each face. So, we have 2 * the area of one of the bases. And we multiply the area of one of the bases by two because when it comes to prisms, we have two congruent and parallel bases. So, they are the exact same size and shape. So if we find the area to the area of one of them, we can multiply it by two in order to get the area of both of them, then we have plus rectangle plus rectangle plus rectangle. So each one of those rectangles, that means the area of rectangle. So we'll talk more about what those rectangles mean here in minute. So let's jump into number one here. And the first thing we need to do is find the area of the base here and then multiply it by two. So our bases are triangles for triangular prism. So this front triangle here and the back. And again, they are the exact same size and shape. So we only need to find the area of one. That means we have the area of both. So we'll start with area equals 12 base * height. That's the formula for the area of triangle. So let's plug in now. So 12 times the base is 6 here. So 6 * the height which is that dashed line and the height is 4 in. So let's solve 6 * 4 is 24 * half is 12. So we have 12 square in there and we multiply that by two again because we have two bases and they are the exact same size and shape. So let's write everything out down here below the problem. So surface area equals and we will plug in our first area 12 square in. And now we get to the rectangles. But before we start that want to take look at the right hand side of your screen. And we have our triangular prism unfolded. That's called net. So everything's unfolded. It's going to give us better idea of the areas of the faces and it helps us visualize what we're doing here when we unfold that 3D shape. So, try to visualize unfolding it or even folding that net back up and creating the 3D triangular prism. So, let's get into the rectangles. So, we have bottom rectangle, left rectangle, and right rectangle. Now the left and right rectangle are the exact same size. The bottom one is different. So let's do the bottom rectangle first. So we can think of this as the bottom rectangle here, the right and the left. It doesn't matter what order you do them in. You'll get the same answer either way, but we're starting with the bottom. So let me fill in trying to find some room here. We'll do area equals length * width. So length time width for the area of rectangle. You can also use base time height. So whatever works best for you. So let's plug in area equals well the length is 7 in here and the width is 6 in. So we have 7x6 rectangle or 6x7. either way it will give you the same answer. So 7 * 6 and our area equ= 42 square in for that bottom rectangle. So we'll plug in here 42 and let's actually write on our net here. This is going to be 42 square in. The front triangle remember is 12 square in. And the back triangle is the same. So let's do the right and left. And these rectangles are the exact same. So, we only need to write out one here. So, let's go to the bottom of the screen. Area equals length * width. And let's plug in. So, we have length of seven and width of five here. So, if you're having trouble picturing the rectangle, it's this right rectangle here. So, 7* 5. Or if you did 5* 7, you'll get the same answer either way. So area equals 35 square in. So 35 and again this is the right one we did but the left one is the exact same in the case of this triangular prism. So 35 square in. So let's add another 35. And now we are good to go as far as adding this up. So we get 2 * 12 is 24 + 42 is 66 and then we have 35 + 35 which is 70. So this is 66 here this is 70. Add those together and we get 136. So surface area equals 136 and that is square in. Now, that was lot of work there as we went through. Now, the more of these problems you do, the better you'll get and the quicker they'll go. kind of laid everything out and went slowly as to really explain each step. But again, the more you do, the quicker and better you'll get at these. So, just to recap, when it comes to finding surface area, find the area of each face, add all of those faces up, and you'll end up with the correct surface area. So, there you have it. There's how you find the surface area of triangular prism. hope that helped. Thanks so much for watching. Until next time, peace.