SOLUTION: A regular triangular pyramid with a slant height of 9m has a volume equal to 50m^3. find the lateral area of pyramid? i really want to know how to solve this, please need help.

Question 969542: A regular triangular pyramid with a slant height of 9m has a volume equal to 50m^3. find the lateral area of pyramid?
i really want to know how to solve this, please need help. i tried but i failed. and dunno where to put this topic, thanks
Answer by rothauserc(4718) (Show Source): You can put this solution on YOUR website!
Lateral area = (1/2) * (perimeter of the base) * (slant height)
A regular triangular pyramid is a regular tetrahedron which is made up of four equilateral triangles
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The slant height is the height(h) of one of the equilateral triangles so by Pythagoras we have
h^2 + (a^2/4) = a^2 where a is the length of a side
9^2 + (a^2/4) = a^2
3a^2/4 = 81
3a^2 = 324
a^2 = 108
a = 10.392304845m approx 10.39m
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perimeter of the base is 3 * (10.39) = 31.17
lateral area = (1/2) * 31.17 * 9 = 140.265 approx 140.27m
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