The pyramid is a polyhedron in which basis the polygon, and other sides - the triangles meeting in the general top lies. The solution of tasks with pyramids in many respects depends on a type of a pyramid. At a rectangular pyramid one of side edges is perpendicular to the basis, this edge also is pyramid height.
Instruction
1. Determine a type of a pyramid by its basis. If in the basis the triangle lies, then it is a triangular rectangular pyramid. If a quadrangle — quadrangular and so on. In classical tasks meet a pyramid which basis either a square, or equilateral/isosceles/rectangular triangles.
2. If in the basis of a pyramid the square lies, find height (it — a pyramid edge) through a rectangular triangle. You remember — in stereometry in drawings the square looks as a parallelogram. For example, the rectangular pyramid of SABCD with top of S which is projected in B square top is given. The edge of SB is perpendicular to the basis plane. Edges of SA and SC are equal among themselves and perpendicular to the parties of AD and DC respectively.
3. If in a task edges of AB and SA are given, find SB height from rectangular ΔSAB on Pythagorean theorem. For this purpose subtract AB square from a square of SA. Take a root. Height of SB is found.
4. If the party of a square of AB, and, for example, diagonal is not given, then you remember a formula:. Also express to d=a·√2 the party of a square from formulas of the area, the perimeter entered and the described radiuses if it is given in a condition.
5. If in a task the edge of AB and ∠SAB is given, use a tangent: tg∠SAB=SB/AB. Express height from a formula, substitute numerical values, thereby having found SB.
6. If the volume and the party of the basis is given, find height, having expressed it from a formula: V=⅓\· S · h. S — the area of the basis, that is AB2; h is the pyramid height, i.e. SB.
7. If in SABC pyramid basis (S is projected in In as in item 2, i.e. SB there is height) the triangle lies and data for the area are specified (the party at an equilateral triangle, the party and the basis or the party and corners at isosceles, legs at rectangular), you find height from a volume formula: V=⅓\· S·h. Instead of S substitute a formula of the area of a triangle in dependence of its look, then express h.
8. If the apothem of SK of a side of CSA and the party of the basis of AB is given, find SB from a rectangular triangle of SKB. Subtract KB square from a square of SK, receive SB in a square. Take a root and receive height.
9. If the apothem of SK and a corner between SK and KB (∠SKB) is given, use function of a sine. SB height relation to a hypotenuse of SK is equal to sin∠SKB. Express height and substitute numerical values.