You have a cube whose sides measure 1 cm and you section it
with a plane which passes in the vertexs A, B,C (see attachment).
Find the volume of the pyramid formed by sectioning the cube.
The pyramid has 4 faces: 3 isosceles right triangles and 1 equilateral triangle.
Set the pyramid on a table with one the right triangles on the bottom.
The volume of a pyramid is: .V .= .(1/3) × (area of base) × (height)
. . The base is a right triangle with sides 1 and 1; its area is: .½(1)(1) = 1/2
. . The height of the pyramid is 1.
Therefore, the volume is: .V .= .(1/3)(1/2)(1) .= .1/6