Answer:
The altitude is 6.53 cm
Explanation:
A regular tetrahedron is a triangular pyramid having equilateral triangular faces, therefore we have;
Sides of the equilateral triangle = 8 cm
Given that the slant height, the edge of the tetrahedron, and half the base edge of the tetrahedron form a right triangle, we have;
The slant height, h = √(8² - (8/2)²) = √48 = 4×√3
The segment representing the altitude, H, of the tetrahedron forms a right triangle with the edge of the tetrahedron and 2/3×h
Therefore;
8² = H² + (2/3×4×√3)²
H² = 8² - (2/3×4×√3)²
H² = 64 - 64/3 = 128/3
The altitude H = √(128/3) = √6×8/3 = 6.53 cm.