Instruction

1

The formula for finding the height

V = (S*h)/3, where S is the area of the polytope lying at the base

In this case, h can be calculated as:

h = (3*V)/S.

**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

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

b2 = a2 - c2;

c2 = a2 - b2.

**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

h = 3*120/46 = 7.83 cm

Answer: the height of the

Example 2: From

h2 = 152 - 142

h2 = 225 - 196 = 29

h = √29 cm

Answer: the height of the

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 cmExample 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 cmNote

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.

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.

) 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.

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.