How to find the height of the rectangular pyramid

Determine the type of the pyramid at its base. If the base is the triangle, then this triangle rectangular pyramid. If a quadrilateral is quadrilateral and so on. In a classic task meet pyramid, the base of which is either a square or equilateral/isosceles/right triangles.

If the base of the pyramid has a square, find the height (also the edge of the pyramid) through a rectangular triangle. Remember that in solid geometry in the figures of the square looks like a parallelogram. For example, given a rectangular pyramid SABCD with vertex S, which is projected to the vertex of the square B. the SB Edge perpendicular to the ground. The ribs SA and SC are equal and perpendicular sides AD and DC respectively.

If in the problem given edge AB and SA, find the height of rectangular SB ΔSAB Pythagoras. To do this, from square SA subtract the square AB. Extract the root. The height of the SB found.

If not given a square of side AB, and, for example, diagonal, remember the formula: d=a·√2. Also Express the side of the square from the formulas of area, perimeter, inscribed and circumscribed radii, if given in the condition.

If the task of the edge AB and ∠SAB, use tangent: tg∠SAB=SB/AB. Express the formula height, substitute numerical values, thereby finding a SB.

If given the volume and base, find the height, expressing it from the formula: V=⅓·S·h. S — area of the base, that is, AB2; h — the height of the pyramid, i.e. SB.

If the base of the pyramid SABC (S is projected to the In as in section 2, i.e., SB – height) is the triangle and set it in the square (side of equilateral triangle, side and bottom or side and at the corners of an isosceles, the legs have a right angle), find the height from the formula of volume: V=⅓·S·h. For S, substitute the formula of area of triangle according to its kind, then Express h.

If given apofema SK facets of CSA and the Foundation of AB, find the SB of a right triangle SKB. From SK subtract square square KB, will receive the SB in the square. Remove the root and get the height.

If given apofema SK and the angle between SK and KB (∠SKB), use the sine function. The ratio of the SB height to the hypotenuse is equal to SK sin∠SKB. Express the height and substitute numerical values.