Question

The base of a right pyramid is an equilateral triangle of side 4 cm the height of the pyramid is half of its slant height is

Answer 1

Answer

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