If the height is 8 and the slant is 10 of a triangular pyramid, then what is the Base edge length and Lateral edge length?
in Geometry Answers by

Your answer

Your name to display (optional):
Privacy: Your email address will only be used for sending these notifications.
Anti-spam verification:
To avoid this verification in future, please log in or register.

1 Answer

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).

 

by Top Rated User (1.0m points)

Related questions

Welcome to MathHomeworkAnswers.org, where students, teachers and math enthusiasts can ask and answer any math question. Get help and answers to any math problem including algebra, trigonometry, geometry, calculus, trigonometry, fractions, solving expression, simplifying expressions and more. Get answers to math questions. Help is always 100% free!
87,021 questions
96,302 answers
2,362 comments
24,339 users