Math Is Fun Forum

MoyMarian

Member

Registered: 2009-01-10

Posts: 29

Regular Square Pyramid

Find the area of the base of regular square pyramid whose lateral faces are equilateral triangles and whose altitude is 20cm.

JurassicPlank

Guest

Re: Regular Square Pyramid

Test!

JurassicPlank

Guest

Re: Regular Square Pyramid

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

JaneFairfax

Member

Registered: 2007-02-23

Posts: 6,868

Re: Regular Square Pyramid

@MoyMarian

It looks like JurassicPlank1 is trying to do your homework for you. Beware, though. For example, JurassicPlank1’s 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 else’s mistakes!

Last edited by JaneFairfax (2009-02-14 08:50:24)