in geometry, how do you find the lateral and base edge of a pyramid?

Question

its a regular polygon

Answer 1

Depends on whether the base is regular or irregular. If the base is irregular, then you must measure each base edge because they could all be different. If it is a regular polygon, then each base edge is the same. If you are not given any info, then you have no recourse but to measure an edge.

A lateral edge requires you to know the height of the pyramid and the distance from the center of the base to a base vertex. Then you can use the Pythagorean theorem.

Answer 2

Firstly , make a fairly large sketch of your square pyramid : It should be large enough to show the height segment, going from the top to the very center of the square base. Some labels : base = b ( so one half of the base length is b/2) the slant height is s the corner length ( usually "c" is your "lateral edge, " l" and the height will be h You have to draw and use two different right triangles ( Note : the legs of a right triangle are the two sides which touch the right angle, the hypotenuse is the third, longest side ) The first right triangle, an inner triangle, has one leg as height h, and the second leg going from the center of the base to the middle of the side( b/2) . Its hyp is the slant height , s and (b/2)^2 + h^2 = s^2 The second right triangle( outer) is drawn on the side : It has a leg of b/2 , going to the bottom corner, a second leg of length "s" going to the top vertex, and a hyp of length " lateral edge " or "l" along the edge. and (b/2)^2 + s^2 = l^2 You use one or the other of these two triangles, and the Pythagoreas expressions to solve all the parts of this problem : Part 1 : inner triangle : h = 4, s = 5 so by pyth, other leg, b/2 is 3 so b = 2(3) =6 Outer Triangle : s = 5 , b/2 = 3 so 5^2 + 3^2 = l^2 so l = √(25 +9 ) = √34 Second question : your 1) Given height and base edge you can find b/2 and then on the inner triangle, the s as hypotenuse of the inner triangle Once you have the slant height, and (b/2) you can use the outer triangle to find "l" Third question : your 2) On the outer triangle, given the s and l you can find the third leg, b/2 Multiplying by 2 will give the base edge, b . On the inner triangle, you can use the just found b/2 and the given s , to find the height leg, h : [ (b/2)^2 + h^2 = s^2 ] so h = √[(s^2 - (b/2)^2 ]

Answer 3

Use Pythagoreon therom, if i could see the question i could help you further.