Advice 1: How to determine the height of the pyramid

Under the pyramid implies one of the varieties of polyhedra whose base is the polygon and its sides are triangles, which are joined into a single, common vertex. If from the vertex drop a perpendicular to the base of the pyramid, the resulting cut will be called the height of the pyramid. To determine the height of the pyramid very easily. Instruction
1
The formula for finding the height of a pyramid is possible to Express the formula then calculate the volume:
V = (S*h)/3, where S is the area of the polytope lying at the base of the pyramid, h is the height of this pyramid.
In this case, h can be calculated as:
h = (3*V)/S.
2
In that case, if the base of the pyramid has a square, length of its diagonal and the edge length of this pyramid, the height of this pyramid can be expressed from Pythagorean theorem, because the triangle which is formed by an edge of the pyramid, the height and half the diagonal of the square at the base is a right triangle.
The Pythagorean theorem States that the square of the hypotenuse in a right triangle, the is equal to the sum of the squares of the other two sides(a2 = b2 + c2). The face of the pyramid is the hypotenuse, one leg is half diagonal of the square. Then the length of the unknown side (height) is by the formula:
b2 = a2 - c2;
c2 = a2 - b2.
3
To both situations was the most clear and understandable, you can consider a couple of examples.
Example 1: Area of base of the pyramid 46 cm2, its volume is 120 cm3. Based on these data, the height of the pyramid is this:
h = 3*120/46 = 7.83 cm
Answer: the height of the pyramid will be approximately 7.83 cm
Example 2: From the pyramid, which lies at the base a regular polygon is a square, its diagonal is 14 cm, the length of the edge is 15 cm According to the to find the height of the pyramid, you need to use the following formula (which appeared as a consequence of the Pythagorean theorem):
h2 = 152 - 142
h2 = 225 - 196 = 29
h = √29 cm
Answer: the height of the pyramid is √29 cm or approximately 5.4 cm
Note
If the base of the pyramid is a square or other regular polygon, the pyramid can be called correct. This pyramid has several properties:
its lateral edges are equal;
face it - isosceles triangles, which are equal to each other;
around this pyramid to describe the sphere and enter it.

Advice 2 : How to find the edge length of a pyramid

The pyramid is a figure that has a base in the form of a polygon and the lateral faces converging at the top with peaks. The boundaries of the lateral faces are called edges. And how to find the length of the edges of the pyramid? Instruction
1
Find the boundary points of the ribs, the length of which are looking for. Let it be points A and B.
2
Set the coordinates of the points A and B. They need to ask three-dimensional, because the pyramid three – dimensional figure. Get A(x1, Y1, z1) and B(x2, y2, z2).
3
Calculate the needed length, using the General formula: edge length of a pyramid is equal to square root of the sum of squares of differences of corresponding coordinates of boundary points. Substitute the numbers for your coordinates into the formula and find the length of the edges of the pyramid. In the same way, find the length of the ribs is not only the right of the pyramid, but rectangular, and truncated and arbitrary.
4
Find the length of the edges of the pyramid, in which all edges are equal, set the base figure and known height. Determine the location of the base height, i.e. the lower point. Since edges are equal, then it is possible to draw a circle whose center is the intersection point of the diagonals of the base.
5
Draw straight lines connecting the opposite corners of the base of the pyramid. Mark the point where they intersect. This point will be the lower bound of the height of the pyramid.
6
Find the length of diagonal of a rectangle using the Pythagorean theorem, where the sum of the squares of the legs of a right triangle is equal to the square of the hypotenuse. Get A2+b2=c2, where a and b are the legs and C is the hypotenuse. The hypotenuse will then be equal to the square root of the sum of the squares of the legs.
7
Find the length of the edges of the pyramid. First divide the length of the diagonal in half. All the data, substitute values in the formula of Pythagoras, are described above. Similar to the previous example, find the square root of the sum of the squares of the height of the pyramid and the half-diagonal.

Advice 3 : How to find the lateral edge of the pyramid

A pyramid is a polyhedron whose faces are triangles having a common vertex. The calculation of the lateral edges is taught in school, in practice often it is necessary to remember forgotten the formula. Instruction
1
Referring to the Foundation of the pyramid can be triangular, rectangular etc. Triangular pyramid known as a tetrahedron. In the tetrahedron, any face can be taken as a basis.
2
The pyramid is right, rectangular, truncated, etc. regular pyramid is called in that case, if its base is a regular polygon. Then the center of the pyramid is projected onto the center of the polygon and the lateral edges of the pyramid are equal. In such a pyramid the lateral faces are identical isosceles triangles.
3
A rectangular pyramid is called when one of its edges perpendicular to the base. The height of this pyramid is exactly that edge. The calculations of the height values of the rectangular pyramid of the lengths of its side edges lying everyone knows the Pythagorean theorem.
4
To calculate the edges of a regular pyramid you need to hold the height of the top of the pyramid to the base. Next, consider the desired fin as a leg in a right triangle using the Pythagorean theorem.
5
The side edge in this case is calculated by the formula b=√ h2+ (a2•sin (180°
) 2. It is the square root of the sum of the squares of two sides of a right triangle. One side is the height of the pyramid h, the other side is a segment connecting the center of the base of a regular pyramid with the peak of this reason. In this case, the a – side of a regular polygon base, n is the number of sides.
Note
Description of the pyramids and the study of its properties was begun in Ancient Greece. Today, the elements of the pyramid, its properties and the laws of the construction studied at school on geometry lessons.

The main elements of a pyramid are lateral faces are triangles that share a vertex; the lateral edges – the sides that are common; apofema (height-side edge held from the top, assuming that the pyramid is correct), the top of the pyramid - the point where the lateral edges etc.
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