SOLUTION: How many inches long is the altitude of a regular triangular pyramid the base is 12 inches on a side and its volume is 103.8 cubic inches. Round off the answer to the nearest integ

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Question 1198303: How many inches long is the altitude of a regular triangular pyramid the base is 12 inches on a side and its volume is 103.8 cubic inches. Round off the answer to the nearest integer.
Answer by greenestamps(13216) About Me  (Show Source):
You can put this solution on YOUR website!


Volume of a pyramid: one-third area of base, times height (altitude).

The base is an equilateral triangle with side length 12. A quick formula for the area of an equilateral triangle with side length s is %28s%5E2%2Asqrt%283%29%29%2F4. So


h=103.8%2F%2812%2Asqrt%283%29%29+=+5

The result of the actual calculation to 3 decimal places is 4.994; we can assume that the actual height is 5 inches and the given volume of 103.8 cubic inches is approximate.