How to Calculate the Surface Area of a Square Pyramid

Video Transcript

"Hi, I'm Steve Jones and I'd like to show you how to calculate the surface area of a square pyramid. Now, this is a square pyramid. The base is square in section. Length of the side B and B. The height of the pyramid is H with a slant height S to a point at the top here to the vertex at the top. So, first of all, we can see that on this pyramid there are actually five faces. Two slanting faces at the front. Two that we can't see and the base. So, there are five all together. Five faces. The first four faces are all the same. They have a width B, a slant height S and they are triangular. So, triangular with a base length B and height S is half BS for the area of a single triangle, half of the base times the slant height, and we must divide that by four to get the area or vol of the sloping faces, and this four times the half BS which is two B times S. The base is a simple square, and the length of the side of the square is B. So, the base is B times B which is B squared, and that will be square centimeters later on when we do the calculation. So, the total area is two BS plus B squared. Let's try that now with B at two centimeters and S at four centimeters. So, the area is going to be two times B which is two times S which is four plus B squared, and remember B squared is B times B; two times two. Now, remember multiplication before addition. So, we have to multiply these out. Two times two times four. I think you'll find is sixteen plus two times two is four. So, the total area is sixteen plus four which is twenty. It's an area centimeters squared. So, this is simply how to calculate the surface area of a square pyramid."