hey guys today we are going to review how to find the volume of prisms and pyramids so let's start with rectangular prisms to find the volume of a prism we're going to use the formula V equals area of the base times the height and our base in a rectangular prism is a rectangle so we're just going to multiply the two side lengths that form a right angle in our base remember rectangular prisms are special because you can use any of the opposite faces as the base you just have to make sure that you Circle the height as the distance between those two bases so I could have used those two that I just highlighted I'm going to use these two as my bases this time which makes my height nine so my volume formula for rectangular prism is V equals area of the base times the height I just circled my height as nine so I'm going to plug that in and then cross it out so I don't accidentally use it again and now I'm going to find B the area of the rectangular base by doing 3 times 11. so the area of the base is 33. so I'm going to plug that into the formula so now to find the volume I will do 33 times 9. so the volume of this rectangular prism is 297 millimeters cubed okay next I have a triangular prism it's the same formula V equals area of the base times the height but this time my base is a triangle so we need to do the base times height divided by 2 to find the area of the triangle so let's find the volume of this triangular prism it's going to be V equals area of the base times the height my bases are these triangles so that means my height is 10 since that's the distance between them now I just need to find the area of the base by doing the base times the height of the triangle divided by 2. so the base of the triangle is going to be 8 meters because that forms a right angle with the six meters so to find the area of the base I will do 8 times 6 divided by 2 which is a 48 divided by 2 which is 24. so the area of the base is 24 so to find the volume I do 24 times 10 so the volume of this triangular prism is 240 meters cubed okay now I get into pyramids it is similar except I'm going to have a one-third since it's a pyramid instead of a prism so let's start with the rectangular pyramid I'm going to do 1 3 times the area of the base which is going to be a rectangle so I'll just multiply the length and the width through the base and height times the height of the pyramid so let's practice finding the volume of this rectangular pyramid I'm going to use the formula V equals 1 3 times the area of the base times the height and the base of this pyramid is a rectangle and the height is 12. so I'm going to plug that into my formula and then cross it out so I don't accidentally use it again and now I'm going to find the area of the rectangle by doing 7 times 3 since those are the dimensions of the rectangle which is 21. so I'm going to plug that in for 21 and I'm going to fill out the rest of this formula so to find the volume I'll do 1 3 times 21 times 12. 1 3 times 21 is 7 so the volume will be 7 times 12 which is 84. so the volume of this rectangular pyramid is 84 centimeters cubed okay then last one triangular pyramid it's the same Formula 1 3 area of the base times the height of the prism the base is a triangle so I will do base times height divided by 2 to find the area of the base so let's practice finding the volume of this triangular pyramid by doing V equals one third times the area of the base times the height my base is this triangle here and that makes the height of this pyramid 21 so I'm going to plug that in for H into my formula and then cross it out so I don't use it again and now I'm going to find B the area of the Triangular Base by doing the base of the triangle which is 30 times the height of the triangle which is 10. so it'll be 30 times 10 divided by 2 30 times 10 is 300 so the area of the base is 300 divided by 2 which is 150. so I'm going to plug that in for B into my formula so the volume will be 1 3 times 150 times 21. so 1 3 times 150 is 50. so the volume can be found by doing 50 times 21. so the volume of this rectangular pyramid is 1050 inches cubed