A regular triangular pyramid with a slant height of 9 m has a volume equal to 50 m3.
Find the lateral area of the pyramid.
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A regular triangular pyramid with a slant height of 9 m has a volume equal to 50 m3.
Find the lateral area of the pyramid.
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Answer:
lateral area of the pyramid = 140.265 approx. 140.27m
Step-by-step explanation:
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
perimeter of the base is 3 * (10.39) = 31.17
lateral area = (1/2) * 31.17 * 9 = 140.265 approx. 140.27m