Find the slant height of this square pyramid.

Solution:

The base of the pyramid is a square.

The sides of the square pyramid has all edges s = 6”

The triangular faces of the square pyramid are equilateral triangles.

The slant height of the pyramid is an altitude of the triangular face which is perpendicular to the base of of the base of the triangular face and also bisects it.

(Length of Pyramid Edge)² = (Length of Slant height)² + (1/2 × edge of the square base)²

(6)² = (Length of Slant Height)² + (1/2 × 6)² 

(Length of Slant height)² = 36 - (3)² = 36 - 9

(Slant height)² = 27

Slant Height = √27 = √9 × 3 = 3√3

Find the slant height of this square pyramid.

Summary:

The slant height of this square pyramid is 3√3