SOLUTION: The base of a pyramid is the regular polygon ABCDEFGH, which has 14-inch sides.All eight of the pyramid’s lateral edges,VA,V B, . . . ,V H, are 25 inches long. To the nearestten

Question 1163749: The base of a pyramid is the regular polygon ABCDEFGH, which has 14-inch sides.All eight of the pyramid’s lateral edges,VA,V B, . . . ,V H, are 25 inches long. To the nearesttenth of an inch, calculate the height of pyramid VABCDEFGH.
Answer by greenestamps(13216) (Show Source): You can put this solution on YOUR website!

Let P be the center of the regular octagonal base. Then triangle APV is a right triangle you can use to find the height of the pyramid.

Let's see what you need to do to find that height.

You know AV is 25; to determine PV, you need to find AP.

Diagonal AE of the base passes through P; the length of AP is half of AE. So you need to find AE.

You can use right triangle ADE of the base to do that. You know the length of DE is 14; you need to know the length of AD.

To find the length of AD, divide trapezoid ABCD into a rectangle and two isosceles right triangles and use the known length of side BC.

The discussion to this point was "backwards", determining what you need to do to find the volume. Now let's put the steps in order.

(1) Use trapezoid ABCD and the known length of BC to determine the length of AD.
(2) Use AD and DE in triangle ADE to determine AE.
(3) Cut AE in half to get AP.
(4) Use AP and AV to find the height, PV.

NOTE: The numbers in the problem are not "nice". Use a calculator to do the calculations; and don't do any rounding until the final answer.

If you need more help with this, re-post the problem, showing how far you have gotten in the work.

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