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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 in².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 = = = .
If the area of the section is 8.5 , then you can find the altitude H of the original pyramid from the proportion
= ,
where h is the height of the small (cut) pyramid, and we know that h = 8-6 = 2 in. So, your proportion is
= .
Please complete the calculations yourself.