Volume of a pyramid-Geometry Help

hi welcome to moomoomath today we're going to look at how to find the volume of a pyramid first of all what is a pyramid a pyramid is a 3d figure that has a base and it has an apex and has a point basically i always think of the egyptian pyramids um to decide what's a pyramid and what's a prism because those are very confusing to students so a pyramid has a point at the top and a prism has parallel bases top and bottom okay but the volume of these and to find the volume of these is very very similar okay the volume of a prism is one is equal to the base area times the height now the difference between that and a pyramid is we're going to take one third of that volume so we're going to actually find the volume of the prism and then divide it by three or multiply it by one third so let's look at some different types of bases first you can have a square base so the area of the base would be just side squared so in this base area formula for a square base you would just plug in side squared times the height and then multiply it by 1 3 or divided by 3. if you had like a right triangular base you would take one half the base times the height of the this part of the pyramid and then you would take that one-half base times height of the base and then multiply that times the height of the whole pyramid or the altitude of the pyramid and you could have something like this which is a rectangular base and to find the area of a rectangle you're just going to take base times height so if you're looking down straight on it it's just base times height of the base and that gives you the base area and then you're going to multiply it times the altitude or the height of the actual um pyramid so you're going to take one or one-third the base times the height when you're just looking at the base and then you're going to multiply it times the height of the pyramid or the altitude so there are three different figures in three different formulas that go in to find the volume so let's take one of these let's look at just the the one that has a square base let's say the side of the square is four and we know that the altitude or the height inside is 5 what would the volume be well you're just going to plug in 4 squared and times 5 so that's going to be 16 times 5 which is 80 but then we have to take one third of the volume so we're going to multiply it by one third which is the same as dividing by three so that's 80 thirds would be the volume and you could leave it like that or put it in your calculator 80 divided by 3 to get the decimal okay so there's one example let's look at this right triangular base this one gives students trouble okay let's say that we have one side of the base is eight this side is six well if this is where the right angle is we know that these are the legs so we're going to look at that let's redraw it over here all we need to do is find the area of that triangle the area of that triangle is one half the base which is six times a height which is eight half of six is three and three times eight is twenty-four so that's the base area of this triangular base and let's draw an altitude let's say the altitude is seven we're gonna take that plug it in over here into the formula one third the base area we just use that one half base times height to figure out it's 24 times the height of the pyramid which is seven so one third of 24 is like 24 divided by three so that's eight and eight times seven is 50 so that's units cubed and that's how you would find the volume of the pyramid oh yeah that's it i hope this video is helpful