The base of a prism is one of its congruent sides. Since all opposite sides of a rectangular prism are congruent, any side can be used as the base, as long as you are consistent in your calculations.
For example, if you know the volume of the prism is 64 cubic meters (m3{\displaystyle m^{3}}), then your formula will look like this:64=Ah{\displaystyle 64=Ah}
For example, if the base is a rectangle with a length of 8 meters and a width of 2 meters, to find the area you would calculate:A=(8)(2){\displaystyle A=(8)(2)}A=16m2{\displaystyle A=16m^{2}}
For example, if you found the area of the base to be 16 square meters, then your formula will look like this:64=16h{\displaystyle 64=16h}
For example, if your equation is 64=16h{\displaystyle 64=16h}, you would need to divide each side by 16 to find h{\displaystyle h}. Thus:6416=16h16{\displaystyle {\frac {64}{16}}={\frac {16h}{16}}}4=h{\displaystyle 4=h}So, the height of your rectangular prism would be 4 meters.
The base of a prism is one of its congruent sides. The base of a triangular prism will be a triangle. The sides will be rectangles.
For example, if you know the volume of the prism is 840 cubic meters (m3{\displaystyle m^{3}}), then your formula will look like this:840=Ah{\displaystyle 840=Ah}
Alternatively, if you know the length of all three sides of a triangle, you can find the area using Heron’s formula. [6] X Research source Read Calculate the Area of a Triangle for complete instructions. For example, if the base of the triangle is 12 meters, and the height of the triangle is 7 meters, to find the area you would calculate:A=12(12)(7){\displaystyle A={\frac {1}{2}}(12)(7)}A=12(84){\displaystyle A={\frac {1}{2}}(84)}A=42{\displaystyle A=42}
For example, if you found the area of the base to be 42 square meters, then your formula will look like this:840=42h{\displaystyle 840=42h}
For example, if your equation is 840=42h{\displaystyle 840=42h}, you would need to divide each side by 42 to find h{\displaystyle h}. Thus:84042=42h42{\displaystyle {\frac {840}{42}}={\frac {42h}{42}}}20=h{\displaystyle 20=h} So, the height of your triangular prism would be 20 meters.
In order for this method to work you must know the surface area of the prism, as well as the length and width of the base.
For example, if you know the surface area is 1460 square centimeters, your formula will look like this:1460=2B+Ph{\displaystyle 1460=2B+Ph}
For example, if the base is a rectangle with a length of 8 centimeters and a width of 2 centimeters, to find the area you would calculate:A=(8)(2){\displaystyle A=(8)(2)}A=16{\displaystyle A=16}
For example, if you found the area of the base to be 16, your formula will look like this:1460=2(16)+Ph{\displaystyle 1460=2(16)+Ph}1460=32+Ph{\displaystyle 1460=32+Ph}
Remember that opposite sides of a rectangle have the same length. [8] X Research source For example, if the base is a rectangle with a length of 8 centimeters and a width of 2 centimeters, to find the perimeter you would calculate:P=8+2+8+2{\displaystyle P=8+2+8+2}P=20{\displaystyle P=20}
For example, if you found the perimeter of the base to be 20, your formula will look like this:1460=32+20h{\displaystyle 1460=32+20h}
For example, if your equation is 1460=32+20h{\displaystyle 1460=32+20h}, you would first need to subtract 32 from each side, then divide each side by 20. Thus:1460=32+20h{\displaystyle 1460=32+20h}1428=20h{\displaystyle 1428=20h}142820=20h20{\displaystyle {\frac {1428}{20}}={\frac {20h}{20}}}71. 4=h{\displaystyle 71. 4=h} So, the height of your prism is 71. 4 centimeters.
In order for this method to work you must know the surface area of the prism, as well as the area of the triangular base, and the length of all three sides of the base.
For example, if you know the surface area is 1460 square centimeters, your formula will look like this:1460=2B+Ph{\displaystyle 1460=2B+Ph}
Alternatively, if you know the length of all three sides of a triangle, you can find the area using Heron’s formula. [10] X Research source Read Calculate the Area of a Triangle for complete instructions. For example, if the base of the triangle is 8 centimeters, and the height of the triangle is 4 centimeters, to find the area you would calculate:A=12(8)(4){\displaystyle A={\frac {1}{2}}(8)(4)}A=12(32){\displaystyle A={\frac {1}{2}}(32)}A=16{\displaystyle A=16}
For example, if you found the area of the base to be 16, your formula will look like this:1460=2(16)+Ph{\displaystyle 1460=2(16)+Ph}1460=32+Ph{\displaystyle 1460=32+Ph}
For example, if the base is a triangle has three sides with lengths of 8, 4, and 9 centimeters, to find the perimeter you would calculate:P=8+4+9{\displaystyle P=8+4+9}P=21{\displaystyle P=21}
For example, if you found the perimeter of the base to be 21, your formula will look like this:1460=32+21h{\displaystyle 1460=32+21h}
For example, if your equation is 1460=32+21h{\displaystyle 1460=32+21h}, you would first need to subtract 32 from each side, then divide each side by 21. Thus:1460=32+21h{\displaystyle 1460=32+21h}1428=21h{\displaystyle 1428=21h}142821=21h21{\displaystyle {\frac {1428}{21}}={\frac {21h}{21}}}68=h{\displaystyle 68=h} So, the height of your prism is 68 centimeters.
