If a pyramid of.base B has itd vertex at any point in a plane parallel to and distant h from thr plane of the base,find its volume.

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You need to calculate the slant height of the pyramid for the formula of the lateral area. You should find a value of (1/2)*SQRT(203) or about 7.1239 cm



You need to calculate the altitude (height) of the pyramid from the apex (summit) to the center of the base triangle (center of inscribed circle, barycenter, orthocenter). The hypotenuse of such triangle is the slant height. One leg is the altitude (to be found), the measure of the second leg is (1/3) the altitude of the equilateral triangle that forms the base. You should find (1/3) m MH= (1/3)* (11/2)*SQRT(3)


1. Calculate the area of the base (use a formula for the equilateral triangle or the general formula for a triangle: you have its height MH ).
2. Lateral area = 3 times the area of triangle Triangle ECD (in yellow above).
3. Total area = area of base + lateral area.
4. Volume= (1/3)(Area of base)* (height of pyramid)
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Good question, and I cannot answer it... but my first thought is, it is not a perfect pyramid. But, if it were, and I wanted to figure it out, I would do a Google search for volume of a pyramid. I'm sure there is a formula out there. I got V=(l*w*h)/3. I'm too lazy to get out my calculator and there is no pencil and paper handy. Good question though.

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If the pyramid is made of homogenous material you need not worry about the mass (what you call weight) since the ratio of the masses is equal to the ratio of the volumes.
Setting the ratio of volume to be 1/2, and using the ratio of the base areas of the pyramids to be (x/h)^2, you end up with
(1/2)=(x/h)^3
Solving for x, you get x=h/(cubic root of 2)

I assume you mean a square base.

2.0833 litres.

If this is homework, be sure to show your work.

2.0833 litres.

If this is homework, be sure to show your work.

You need 5 isosceles triangles with a base of 30 mm. To get the height of the triangles (perpendicular to the 30 mm bases) you need to calculate the apothem of the pentagon (assumed to be regular).

If you cut the pyramid by a plane passing through its apex, the center of the base-pentagon,and the midpoint of one side, the plane figure created by the three points (apex, center, and midpoint) is a right triangle. The legs are the apothem, and the altitude of the pyramid. The hypotenuse is the slant height of the pyramid, and is thus the height of the triangles in the development. pyramid (60 mm) form.
Use the Pythagorean Theorem to find that slant height.
s^2=a^2+h^2.

The plane area shown in what figure?

A pyramid is made of triangles, and the number of triangles for a particular pyramid base. For a square base pyramid - 4 triangles; pentagonal base - 5 triangles

find the volume of the largest cylinder with circular base that can be incribed in a cube whose volume is 27cu.in?