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.