RightTriangular Pyramid VolumeVolume of a Pyramid with RightTriangular BaseResult:0.5


base (b)  units  

height (h)  decimals  
Height (H)  
A rightangle triangular pyramid with a base of 3 units a triangle height of 4 units and a pyramid height of 5 units has a volume of 10 cubic units.
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A righttriangular pyramid is a three dimensional shape with a rightangle triangle at its base extruding up to a single point. The volume of a righttriangular pyramid can be calculated according to the following formula:
V = 1/3(Ah)
where A = 1/2(bh) (standard righttriangle)
so : V = 1/6(bhH)
Explanation: The general formula used to find the volume of a pyramid is onethird times area of the base times height of the pyramid. Because it is known that this pyramid has a righttriangle at its base the formula for a righttriangle is used to calculate the area. The formula onehalf base times height is inserted into the volume formula in the place of area. After multiplying out the formula now reads onesixth time base of triangle (b) times height of triangle (h) times height of pyramid (H).
Below is an example of how to find the volume of this type of triangular pyramid. In this example the triangle at the base of the pyramid must have a ninety degree (right) angle. Lets say the triangle has a base of 3 meters, a height of 4 meters and that the pyramid is 5 meters tall: