SOLUTION: Given square pyramid: square ABCD with base side AB = 2cm, and height EO = 3cm. Find the exact length of AC and the exact length of EC. F is the midpoint of CB. Find the exact sla

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Question 1023319: Given square pyramid: square ABCD with base side AB = 2cm, and height EO = 3cm. Find the exact length of AC and the exact length of EC.
F is the midpoint of CB. Find the exact slant height EF.
Thanks for any help!:) Thank you so much, I'm having a lot of trouble with this question!
Found 2 solutions by Theo, rothauserc:
Answer by Theo(13342) (Show Source):
You can put this solution on YOUR website!
AC is a diagonal of the square base.
as such it's length would be sqrt(2^2 + 2^2) = sqrt(8).
the diagonal AC forms a triangle AEC of which EO is the altitude.
this triangle AEC, with its altitude of EO, forms 2 right triangles.
they are triangle AEO and triangle EOC.
the height of these triangles is 3.
the base of these triangles is sqrt(8)/2.
the hypotenuse of these triangles is equal to sqrt(3^2 + (sqrt(8)/2)^2).
this becomes sqrt(9 + 8/4) which becomes sqrt(36/4 + 8/4) which becomes sqrt(44/4) which becomes sqrt(44)/2 which becomes sqrt(4*11)/2 which becomes 2*sqrt(11)/2 which becomes sqrt(11).

you get:

length of AC is sqrt(8).
length of EC is sqrt(11).

the diagram below should help you visualize what's happening.

Answer by rothauserc(4718) (Show Source):
You can put this solution on YOUR website!
we use the Pythagorean Theorem to find these values
:
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slant height = EF
:
slant height^2 = (AB/2)^2 + EO^2
:
slant height^2 = 1 + 9
:
slant height = square root(10) = 3.16 cm
:
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AC^2 = AB^2 + BC^2
:
AC^2 = 4 + 4
:
AC^2 = 8
:
AC = square root(8) = 2.82 cm
:
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EC^2 = slant height^2 + 1^2
:
EC^2 = 10 + 1
:
EC = square root(11) = 3.32 cm
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