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Find the area of the base of regular square pyramid whose lateral faces are equilateral triangles and whose altitude is 20cm.
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Test!
H = 20 cm
For the equilateral triangle (all sides and angles equal)
Length of base = Length of long diagonal = S
Half base length = S/2
Area of base = S²
Project the long diagonal S onto the base 'say' D = S/2cos45
Hence H² + D² = S² (Right angle triangle)
H² = S² - D² = S² - S²/4cos²45 = S²(1 - 1/4cos²45)
S² = H²/(1 - 1/4cos²45)
Substitute H = 20 cm
Area = 400/(1-0.5) = 800 cm²
S = √800 = 28.284 cm
So in simple terms the area of the base = 2H²
@MoyMarian
It looks like JurassicPlank1 is trying to do your homework for you. Beware, though. For example, JurassicPlank1s solution to this problem
http://www.mathisfunforum.com/viewtopic.php?id=11551
is incorrect.
Much better to do your own homework than to copy somebody elses mistakes!
Last edited by JaneFairfax (2009-02-14 08:50:24)
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