Apothem - height of a side side which is carried out in a regular pyramid from its top. It can be found as in a usual regular pyramid, and truncated. Let's consider both cases
Instruction
1. Correct piramidav all side edges are equal to it, side sides are isosceles equal triangles, and the basis – a regular polygon. Since all apothems of a regular pyramid are equal, it is enough to find of one in any triangle. Triangles are isosceles, and the apothem is height. Height which is carried out in an isosceles triangle from top to the basis is a median and a bisector. The median halves the party, and a bisector a corner on two equal corners. Height – the perpendicular which is carried out from top to the basis.
2. All parties of an isosceles triangle are Let's say known and the median which divides the basis into two equal pieces is carried out. Since the median is height, it is a perpendicular, i.e. the corner between a median and the basis is equal 90 degrees. Means, the rectangular triangle turns out. The side is a hypotenuse, a half of the basis and height (median) is legs. Pythagorean theorem says: the square of a hypotenuse is equal to the sum of squares of legs. In such a way it is possible to find height.
3. Let the corner lying opposite to the basis be known. And some one of the parties (either side, or basis). The bisector which is carried out from top to the basis is height. Therefore again the rectangular triangle turns out. The corner and one of the parties is known. By means of a sine, a cosine and a tangent it is possible to find height. A sine – the relation of an opposite leg to a hypotenuse, a leg - the relation of an adjacent leg to a hypotenuse, a tangent – the sine relation to a cosine or an opposite leg to adjacent. Having substituted the known parties, calculate height. The area of a side surface of a regular pyramid is equal to a half of the work of perimeter of the basis on an apothem.
4. Correct truncated piramidabokovy sides there are correct trapezes. Side edges are equal. An apothem – height which is carried out to trapezes. Let two bases and a side edge be known. From top heights are carried out so that on the bigger basis they cut a rectangle. Then if mentally to remove a rectangle, there will be an isosceles triangle which height can be found on the first way. If obtuse angles of a trapeze are known, then when carrying out height, it is necessary to subtract a corner, equal 90 degrees (since height is a perpendicular) from stupid. Then the acute angle in a triangle will become known. Height or an apothem besides can be found on 1 way.