What are the properties of a quadrangular pyramid and what are the properties of a quadrangular pyra

Regular quadrangular pyramid: all four sides are isosceles triangles, which are special quadrangular pyramids; The projection of the vertex on the bottom surface is the center of the square, and the sides and edges are equal to the dihedral and included angles of the bottom surface.

Regular triangular pyramid: the bottom surface is an equilateral triangle, the three lateral edges are equal, and the projection of the vertex on the bottom surface is the center of the triangle [i.e., the inner [equal distance to the three sides], the outer center [the three vertices on the bottom are equally distanced], and the center is the outer center, the inner center, or the vertical center]; The dihedral angles and angles of each side and each side edge are equal to the bottom surface; The center of the outer ball is the same point as the center of the inner ball, and the distance from the center of the ball to the vertex is equal to twice the distance to the surface, i.e., the center of the outer ball is twice the length of the radius of the center of the inside ball. Regular pyramid:

All four sides are square, which is a special regular triangular pyramid; The projection of the vertex on the bottom is the center of the triangle [i.e., the inner [equal distance to the three sides], the outer center [equal distance to the three vertices on the bottom], and the center is the outer center, inner or perpendicular center]; The dihedral angles and angles of each side and each side edge are equal to the bottom surface; The center of the inscribed ball is at the same point as the center of the inscribed ball, and the distance from the center of the ball to the vertex is equal to three times the distance to the surface, i.e., the center of the outer ball is three times the length of the radius of the center of the inscribed ball. Regular triangular prism: the bottom surface is an equilateral triangle, the side edges are equal and parallel, and both are perpendicular to the bottom surface, and the sides are rectangular, and the upper and lower sides are parallel to each other.

Regular quadrangular prism: the bottom surface is square, the side edges are equal and parallel, and all are perpendicular to the bottom surface, and the sides are rectangular, and the upper and lower sides are parallel to each other.

This cavity is equal on each side of the pyramid, and all sides are congruentIsosceles triangle, the height of each isosceles triangle is equal (it is called the oblique height of the pyramid); The projection of the height and oblique height of the regular quadrangular pyramid and the oblique height of the source in the bottom surface form a right triangle, and the projection of the height, side edge and side edge of the regular pyramid in the bottom surface also forms a right triangle. The side edge of the regular quadrangular pyramid is formed by the bottom surfaceHornsEqual; The sides of the pyramid are equal to the dihedral angles of the bottom surface.

Regular quadrangular pyramid formula:Volume formula. hs^1/3。

Surface area formula.

s(4h^2+s^2)^(1/2)+s^2。

Side area formula: s(4h2+s2) (1 2).

Base area formula: S2.

where h = height and s = bottom side length.

Note the volume algorithm: the height of the regular quadrangular cone is measured by the distance from the center of the square to the vertex.

Regular quadrangular pyramid: The bottom surface is square, and the sides are 4 stool wheels burning congruent isosceles triangles with common vertices, and the projection of the vertices on the bottom surface is the center of the bottom surface. The bottom surface is a square, and the projection of the top point on the bottom surface is the center of the square.

The bottom edge of the triangle is the side of the square. Volume formula: h*s*1 3 (h=height, s=bottom area).

Volume formula: HS 1 3.

Surface area formula: s(4H2+S2) (1 2)+S2.

Side area formula: s(4h2+s2) (1 2).

1. The edges on each side of the regular quadrangular pyramid are equal, and each side is a congruent isosceles triangle, and the height on the bottom edge of each isosceles triangle is equal (it is called the oblique height of the regular pyramid).

2. The projection of the height, oblique height and oblique height of the regular quadrangular pyramid in the bottom surface of the jujube void forms a right-angled triangle, and the projection of the height, side edge and side edge of the regular pyramid in the bottom surface also forms a right-angled triangle.

3. The angle formed by the side edge of the regular quadrangular pyramid and the bottom surface is equal; The sides of the pyramid are equal to the dihedral angles of the bottom surface.

The above content refers to the Encyclopedia - Regular Quadrangular Pyramid.

A regular triangular pyramid is a triangular pyramid with a regular triangle on the bottom surface of the cone and an isosceles triangle on all three sides. A regular triangular pyramid is not the same as a regular tetrahedron, and a regular tetrahedron must be an equilateral triangle with each face. Quality.

1 The bottom surface is an equilateral triangle.

2 On the sides are three congruent isosceles triangles.

3 The projection of the vertex on the bottom surface is the center of the base triangle (also the center of gravity, vertical center, outer center, and inner center).

4.The following four right-angled triangles are often constructed:

1) A right-angled triangle composed of half of the oblique height, side edge and bottom edge; (including the angle between the side edge and the bottom edge) 2) a right-angled triangle composed of high, oblique height, and oblique high projection; (including the angle between the side and the bottom surface) (3) a right-angled triangle composed of height, side edges, and side edge projections; (including the angle between the side edge and the bottom surface) (4) A right-angled triangle composed of oblique high projection, side edge projection, and half of the bottom edge.

Description: The above right-angled triangle concentrates almost all the elements of a regular triangular pyramid. In the regular triangular pyramid calculation problem, the above right triangle is often taken.

Its essence is that it not only flattens the spatial problem, but also triangulates the plane problem, and also concentrates the known and unknown elements in a right triangle, which is conducive to solving. The bottom surface of the regular tetrahedron is a regular triangle, so the oblique high line is located at any vertex and the midpoint of the bottom edge of the line, and the three lines are in one, so the side center of gravity is located at the high line from the vertex 2 3, you can calculate the distance between the vertex and the center of gravity (the ball and the side tangent point), and know the side length of the regular triangular pyramid, you can calculate the length of the line where the center of the circle is located (that is, the line connecting the vertex and the center of gravity of the bottom surface) according to the Pythagorean theorem, and you can calculate the distance between the bottom surface and the center of the sphere (that is, the radius of the inscribed sphere).

Regular triangular pyramid: The bottom surface is a regular triangle, and the projection of the vertex on the bottom surface is the triangular pyramid in the center of the base triangle (the regular triangular pyramid is not the same as the regular tetrahedron, the regular tetrahedron must be a regular triangle on each face) and the bottom regular triangle.

The properties are as follows. 3 edges are equal, the opposite edge is like (just like it) the vertical side area of the opposite side = bus * bottom edge * 3 2 volume = height * bottom area 3

Regular quadrangular pyramid: all four sides are isosceles triangles, which are special quadrangular pyramids; The projection of the vertex on the bottom surface is the center of the square, and the sides and edges are equal to the dihedral and included angles of the bottom surface.

A triangular pyramid is a cone with a triangular shape at the bottom.

The regular triangular pyramid is a regular triangle on the bottom surface, and the projection of the large point of the top stool on the bottom surface is the triangular pyramid in the center of the bottom triangle (the triangle on the side surface is an isosceles triangle.

And the angle between the faces on the side and the face is equal in pairs).

Tetrahedron. It is a cone, which is a regular triangle on all four sides (with the characteristics of a regular triangular pyramid, and the vertical surface of the jujube source on the side is a regular triangle).

A quadrangular pyramid is a cone, with a quadrangular base.

Regular pyramid:It is a cone with a square base, and the mapping point fixed on the bottom is exactly the intersection of the diagonal lines of the square on the base.

The triangular prism is nothing more than the quadrangular prism, and now the column in the textbook is a cylinder that is parallel to the bottom and the top figure, and the side is perpendicular to the bottom.

A regular triangular pyramid is not necessarily a regular tetrahedron.

But! A regular tetrahedron must be a regular triangular pyramid!

The properties of the regular triangular pyramid are: 1. The bottom of the regular triangular pyramid is a triangle with the edge of the hidden hu.

2. The projection of the apex of the regular triangular pyramid on the bottom surface is the center of the triangle on the bottom surface, and it is also the vertical center and outer center.

The center of gravity, and the heart.

3. The length of the lateral edges of the regular triangular pyramid is equal, so the sides are three congruent isosceles triangles.

4. The triangular pyramid is often constructed with the following four right-angled triangles.

1) A right-angled triangle composed of half of the oblique height, side edge and bottom edge; (including the angle between the side edge and the bottom edge).

2) a right-angled triangle composed of high, oblique height, and oblique high projection; (including the angle between the side and the bottom surface).

3) a right-angled triangle composed of height, lateral edges, and lateral edge projections; (including the angle between the side edge and the bottom surface).

4) A right-angled triangle formed by oblique high projection, side projection, and half of the bottom edge.