SOLUTION: a cutting plane is passed through a right regular hexagonal pyramid whose measure of one base edge is 8 in. if the said plane parallel to and 6 in from the base of the pyramid make

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Question 1018071: a cutting plane is passed through a right regular hexagonal pyramid whose measure of one base edge is 8 in. if the said plane parallel to and 6 in from the base of the pyramid makes a section with an area 18.5 inē.find the altitude of the pyramid
Answer by ikleyn(52884) About Me  (Show Source):
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a cutting plane is passed through a right regular hexagonal pyramid whose measure of one base edge is 8 in. if the said plane parallel to and 6 in from the base of the pyramid makes a section with an area 18.5 inē.find the altitude of the pyramid
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The regular hexagon at the base with the side measure of 8 in has the area of 6 equilateral triangles 
with the side measure of 8 in, i.e S = 6%2A%28%281%2F2%29%2A8%2A8%2A%28sqrt%283%29%2F2%29%29 = 6%2A2%2A8%2Asqrt%283%29 = 96%2Asqrt%283%29 in%5E2.


If the area of the section is 8.5 in%5E2, then you can find the altitude H of the original pyramid from the proportion

h%5E2%2FH%5E2 = 8.5%2FS,

where h is the height of the small (cut) pyramid, and we know that h = 8-6 = 2 in. So, your proportion is

2%5E2%2FH%5E2 = 8.5%2F%2896%2Asqrt%283%29%29.

Please complete the calculations yourself.