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CCSS.Math: ,

let's do some solid geometry volume problems so they tell us shown is a triangular prism and so there's a couple of types of three-dimensional figures that deal with triangles this is what a triangular prism looks like where has a triangle on one two faces and they're kind of separated they're kind of have rectangles in between the other types of triangular three-dimensional figures is you might see pyramids this would be a rectangular pyramid because it has it has a rectangular or it has a square base just like that you could also have a you could also have a triangular pyramid where alt was just literally every side is a triangle so stuff like that but this over here is a triangular prism I don't want to get too much into the shape classification if the base of the triangle B is equal to 7 the height of the triangle H is equal to 3 and the length of the prism L is equal to 4 what is the total volume of the prism so they're saying that the base is equal to 7 so this base this right over here is equal to base is equal to 7 the height of the triangle is equal to 3 so this right over here this distance right over here H is equal to 3 and the length of the prism is equal to 4 so I'm assuming it's this dimension over here is equal to 4 so length is equal to 4 so in this situation what you really just have to do is figure out the area of this triangle right over here we could figure out the area of this triangle and then multiply it by how much you go deep so multiply it by this length so the volume is going to be the area of this triangle let me do it in pink the area of this triangle we know that the area of a triangle is 1/2 times the base times the height so the area this area right over here is going to be 1/2 times the base times the height and then we're going to multiply it by like kind of our depth of this triangular prism so we have a depth of 4 so that we're going to multiply that times the four times this depth times the 4 and we get let's see 1/2 times 4 is 2 so this these guys cancel out you'll just have a 2 and 2 times 3 is 6 6 times 7 is 42 42 and it would be in some type of cubic unit so if these were in I don't know centimeters it would be centimeters cubed but they're not making us focus on the units in this problem let's do another one shown is a cube if each side of the cube or if each side is of equal length x equals 3 what is the total volume of the cube so each side is equal length X which happens to equal to 3 so this side is 3 this side over here X is equal to 3 every side X is equal to 3 so it's actually the same exercise is the triangular prism it's actually a little bit easier when you're dealing with the cube where you really just want to find the area of this surface right over here now this is pretty straightforward this is just a square or you could it would be the base times the height or since they're the same it's just 3 times 3 so the volume is going to be the area of this surface 3 times 3 times the depth times the depth and so we go 3 deep so times so times 3 and so we get 3 times 3 times 3 is 27 or you might recognize this from exponents this is the same thing as 3 to the third power and that's why sometimes if you have something to the third power they'll say you cubed it because literally to find the volume of a cube you take the length of one side and you multiply that number by itself three times one for each dimension one for the length the width and or if I guess through the height the length and the depth depending on how you want to define them so it's literally just three times three times three