Draw a triangular prism taking a 4cm base of equilateral triangle.
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The perpendicular drawn from the apex of the pyramid to the triangular will hit it right at the center of the perpendicular drawn from any vertex of the triangle to the opposite side.
Area of equilateral triangle=3–√4×42=43–√
12×4×x=43–√
12x=3–√
h=52−(3–√)2−−−−−−−−−√=22−−√
Volume=13×base area×height
This actually reminds of the area of a tetrahedron, which is what the figure shows.
V=13×43–√×22−−√=466−−√3
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