Question 1065772: A triangular pyramid has a lateral surface of 225 square centimeters. If the height of the pyramid is greater than 12 centimeters and the base has nine equal sides, what are whole-number possibilities for the height and width of each triangular face?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! lateral surface area doesn't include the area of the base.
if there are 9 equal sides, then there are 9 equal triangles.
that means the area of each triangle is 25 square centimeters.
the formula for the area of a triangle is 1/2 * b * h.
you get 1/2 * b * h = 25
multiply both sides of this equation by 2 and you get b * h = 50
divide both sides of this equation by h and you get b = 50 / h
since b > 12, then 50 / h > 12.
multiply both sides of this equation by h to get 50 > 12 * h.
looks like h is a multiple of 12 and can be 1, 2, 3, or 4.
it can't be 5 because 12 * 5 = 60 > 50.
to test these out, use the formula of 25 = 1/2 * b * h and multiply both sides of it by 2 to get 50 = b * h.
if b = 1, then h = 50 > 12 which is a whole number.
if b = 2, then h = 25 > 12 which is a whole number.
if b = 3, then h = 15 and 5/15 > 12 but is not a whole number.
if b = 4, then h = 12 and 2/12 > 12 but is not a whole number.
if b = 5, then h = 10 which is smaller than 12.
my guess is that the base can either be 1 or 2.
when 1, the height is 50.
when 2, the height is 25.
the area of each triangle is always 25.
the lateral area is always 225.
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