Question

How do we find the volume of a triangular pyramid?

Answer 1

Hint: Triangular pyramid can be defined as the pyramid having a triangular base with triangular faces which meet at a point above the base that is known as the apex. Here we will use the formula of area into third measure which gives the volume of the triangular pyramid.

Complete step-by-step answer:
The volume of a triangular pyramid can be represented as, $ V = \dfrac{1}{3}AH $
Where, A is the area of the triangular base and H is the height of the pyramid.
Let us take an example for a triangular pyramid: The height of the pyramid is $ 10 $ cm and the triangular base has a base of $ 6 $ cm and its height of $ 4 $ cm.
Area of the triangular base, $ A = \dfrac{1}{2}bh $
Place the known values in the above equation –
Area of the triangular base, $ A = \dfrac{1}{2}(6)(4) $
Common factors from the numerator and the denominator cancels each other.
Area of the triangular base, $ A = 12{m^2} $
Now, place the above value in the equation $ V = \dfrac{1}{3}AH $
 $ V = \dfrac{1}{3}(12)(10) $
Common factors from the numerator and the denominator cancels each other.
 $ V = (4)(10) $
Simplify the above expression finding the product of the terms.
 $ V = 40{m^3} $
Hence, if we know the area of the triangular base then it can be efficient to get its volume.

Note: A pyramid with the triangular base is also known as the tetrahedron which has equilateral triangles for each of its faces. Always remember that the volume is measured in cubic units while area is measured in square units.