FORMULAE FOR REGULAR TRIANGULAR PYRAMID

b=base edge length, slant height=h, lateral edge length=e, pyramid height=H.

b²=4(e²-h²) relates base edge length, slant height and lateral edge length.

b²=12(h²-H²) relates base edge length, slant height and pyramid height.

Lateral face area=bh/2. Total lateral area, L=3bh/2. Base area (equilateral triangle)=b²√3/4.

Total surface area=3bh/2+b²√3/4.

Volume of pyramid V=⅓(b²√3/4)√(h²-b²/12)=b²√(12h²-b²)/24.

You may find some of the above useful in solving this type of question.

This question does not state whether the pyramid is regular, but let’s assume it is. Also assume H=8 is the height of the pyramid, not the slant height, h=10.

The formula we need is: b²=12(h²-H²), b²=12(100-64)=12×36=432, b=12√3 (about 20.78).

Since b²=4(e²-h²)=12(h²-H²), e²-h²=3(h²-H²), e²=3h²-3H²+h²=4h²-3H² (which can be added to the list of formulae), so e²=400-192=208, e=4√13 (about 14.42).