[Music] welcome to math with mr j [Music] in this video i'm going to cover how to find the volume of a triangular prism now remember the volume is the amount of space an object takes up and for any prism we can use the formula the area of the base times the height so again the volume for any prism is the area of the base times the height that capital b means the area of the base and that h stands for height now since we're working with triangular prisms we're going to have triangular bases so to find the area of those triangular bases we use the formula base times height divided by two the formula for the area of a triangle so this is a more specific formula over here for triangular prisms again because we're using the formula for the area of the triangular bases base times height divided by two and then we multiply that by the height of the prism so let's jump into number one and take a look at the bases of that triangular prism now the bases of a prism are congruent and parallel polygons in the case of triangular prisms we're going to take a look at the triangles that are congruent and parallel so for number one that triangle up front is congruent and parallel to the triangle in the back now we can't see that full triangle in the back but it is congruent and parallel so congruent means same exact size and shape now we name prisms by their bases that's why we call this a triangular prism because our bases are triangles now the height is going to be the distance between those bases the height isn't necessarily going to be vertical or up and down again it's defined by the distance between those bases so let's find the volume of number one and we'll start by writing out our formula so volume equals base times height divided by 2 which is the formula for the area of a triangle times the height of the prism let's plug in so volume equals well base of the triangle is five centimeters so we'll plug in five times the height of the triangle is four centimeters and let's divide by 2 and multiply by the height of the prism not the height of the triangle we need to find the height of the prism so that's going to be 6 centimeters let's solve so 5 times 4 is 20 divided by 2 is 10. so that's the area of our triangular base 10 times 6 is going to give us 60. so volume equals 60 cubic centimeters again i did 5 times 4 which is 20 divided by 2 is 10 times 6 is 60. so our final answer is 60 cubic centimeters so let's move on to number two and we'll start by writing out our formula so volume equals base times height divided by 2 times the height of the prism now we plug in so the base of our base the triangular base is going to be 10 inches right here so we'll plug in 10 times the height which is 7 inches divided by 2. now the height of the prism the distance between the two bases is going to be three inches so we multiply it by three so we end up with 10 times seven which is 70 70 divided by 2 is 35 so we need to solve 35 times 3 and if we can't solve that using mental math that's okay come to the side in order to work through that problem so let's do 35 times three up here to make sure we get the correct answer three times five is fifteen three times three is nine plus one is ten so we get 105. so our volume is 105 cubic inches and we are done to recap we did 10 times 7 is 70 divided by 2 is 35 and then we did 35 times 3 that 3 is the height of the prism and we got 105. so our final answer volume equals 105 cubic inches so there you have it there's how you find the volume of a triangular prism take the area of our triangular base and multiply it by the height of the prism so i hope that helped thanks so much for watching until next time peace