okay so today we're going to talk about prisms and we're going to learn three formulas well one is actually a review formula the volume of a prism but we're also going to learn lateral area of a prism and total area of a prism so first volume is equal to area of the base times your height so for this this is a rectangular prism so the base for us is this square right here but since we multiply everything together it doesn't really matter what order you multiply in because if you remember multiplication is commutative which means you can do it in any order you want so we're going to do the area of the base which is five oops Time 4 times your perpendicular height now if you look This Is Us taking this prism and standing it up like this so that this is four this is five and this perpendicular height is this eight because this height makes a right angle here so we can use that as our height so times 8 so volume is equal to 5 * 4 which is 20 * 8 so volume is equal to 160 and if we had units it would be units cubed because remember volume is a cubic measurement we're going to do one more practice with volume so for this one our base is our base is this right triangle right here so we're going to do V equals the area of the base which for right triangle it's 1/2 base which is three times our perpendicular height which is four times the height of this prism which would be okay and we're going to multiply that by our height which if you were thinking about this as this triangle being the base and this triangle sitting on the ground like that its height would be this four that's right here so V isal 12 * 4 is 2 2 * 3 is 6 * 4 is 24 so 24 units cubed okay for lateral area you take the perimeter of the base and you multiply it by the height when we find lateral area we're just finding let me get my Shader so I can show you we're just just finding the area of these blocks that go up and down we're not going to find the area of this top block or this bottom block okay just the lateral area that stands straight up and down so when we find this we we're going to take our perimeter of the base which is 6 + 3 + 6 + 3 6 + 3 is 9 + 6 + 3 is 9 so 9 + 9 is 18 so the perimeter of the base times our perpendicular height which is right here seven and if you multiply that you get one 26 and pretend they said this was inches it'd be inches squared because remember area is always a squared unit of measure so if we find total area we're going to we're going to be finding the lateral area which is the area of each one of these um rectangles that wraps around the shape these sides but and we're g to add it to this part these two hexagonal bases right there I hope that helps you see a little bit I know it's kind of hard to tell cuz this isn't a 3D piece of paper but for this we take our lateral area which if you remember it's the perimeter of the base so the perimeter of the the base times your height so our perimeter of our base our base let me just say is a regular hexagon so to find our perimeter all we have to do is take three multiply by six and you get 18 so our perimeter of the base is 18 times our height of the shape which is this five right here times 2 area of the or plus two area of a base and an area of a base of a hexon is hexagon is length length right here time height so this is 3 * 4 so 18 * 5 which is 90 plus 3 * 4 which is 12 2 * 12 so 90 + 2 * 12 is 24 so our total area for this prism is4 uh units squared because remember area is always unit squared well that's all we're going to do with prisms today but make sure you come back because in the next lesson we're going to talk about right circular cylinders