The height of a regular quadrangular prism is equal, and the side of the base is. Everything you need to know about prism (2019)

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"Polyhedron" - Side face. Polyhedra. And the ends of the edges are called the vertices of the polygon. We get a pentagonal prism. A is the vertex of the cube. Rectangular parallelepiped. The face of a cube is a square. Convex polyhedron located on one side of the plane of each of its faces. Prism. AB is an edge of the cube.

"Platonic solids" - Platonic solids. Figures and elements. Platonic - (from the name Plato) purely spiritual, not associated with sensuality (for example, platonic love). Founded the Academy around 385. BC, which existed until 529. AD Plato Plato was born in 428. BC. and died in 347. BC. Lived in Athens, received a comprehensive education.

“Sections of Figures” - Depths various sciences. The required section. Examples of section constructions. Section of a cube by plane. Dots. Let's mark the points. Pyramid. Polyhedra in architecture. Construction of sections of a polyhedron. Definition. Meaning. Section. Section of a cube. Let's go straight. Earth. Let's do direct MK. Construct a cross section of a cube.

“In the world of polyhedra” - Euler’s theorem. Archimedes' bodies. Geometry. Kepler-Poinsot bodies. Ashkinuze's body. Alexandrian lighthouse. Mathematics. Top of the cube. Regular polyhedra. Polyhedra in art. Developments of some polyhedra. The world of polyhedra. Tetrahedron. Faros lighthouse. Polyhedra. Convex polyhedra.

“Methods for constructing sections” - Memo. Working with disks. Cutting plane. Method interior design. Let's consider four cases of constructing sections of a parallelepiped. Construction of sections of polyhedra. The trace is the straight line of intersection of the section plane and the plane of any face of the polyhedron. The parallelepiped has six faces.

“Section of a polyhedron by a plane” - Combined method. Test. Construct a cross section of a cube. Polygons. Construct sections of the prism. The cuts formed a pentagon. Section of a cube. Section of polyhedra. Method of auxiliary sections. Methods for constructing sections. Flat figure. Construct a cross section of the prism. Axiomatic method. A body whose surface consists of finite number flat polygons.

Instructions

If in the conditions of the problem the volume (V) of space is given, limited by edges prisms, and the area of ​​its base (s), to calculate the height (H) use the formula common to the base of any geometric shape. Divide the volume by the area of ​​the base: H=V/s. For example, with a base of 1200 cm³ equal to 150 cm², the height prisms should be equal to 1200/150=8 cm.

If the quadrilateral at the base prisms, has some form the right figure, instead of area in calculations, you can use edge lengths prisms. For example, with a square base, replace the area in the formula of the previous step with the second power of the length of its edge (a):H=V/a². And in the case of the same formula, substitute the product of the lengths of two adjacent edges of the base (a and b): H=V/(a*b).

To calculate height (H) prisms knowledge may be sufficient full area surface (S) and the length of one edge of the base (a). Because total area consists of the areas of two bases and four side faces, and in such a polyhedron with a base, the area of ​​one side surface should be equal to (S-a²)/4. This face has two common edges with square ones known size, which means that to calculate the length of the other edge, divide the resulting area by the side of the square: (S-a²)/(4*a). Since the prism in question is rectangular, the edge of the length you calculated adjoins the bases at an angle of 90°, i.e. coincides with the height of the polyhedron: H=(S-a²)/(4*a).

In the correct height (H), knowing the length of the diagonal (L) and one edge of the base (a) is enough to calculate the height (H). Consider the triangle formed by this diagonal, the diagonal square base and one of the side ribs. The edge here is an unknown quantity that coincides with the desired height, and the diagonal of the square, based on the Pythagorean theorem, is equal to the product of the length of the side and the root of two. In accordance with the same theorem, express the desired quantity (leg) in terms of the length of the diagonal prisms(hypotenuse) base (second leg): H=√(L²-(a*V2)²)=√(L²-2*a²).

Sources:

  • quadrangular prism

A prism is a device that separates normal light into individual colors: red, orange, yellow, green, blue, indigo, violet. This is a translucent object, with a flat surface that refracts light waves depending on their lengths and thanks to this allows you to see light in different colors. Do prism It's pretty easy to do it yourself.

You will need

  • Two sheets of paper
  • Foil
  • Cup
  • CD
  • Coffee table
  • Flashlight
  • Pin

Instructions

Adjust the position of the flashlight and paper until you see a rainbow on the sheets - this is how your beam of light is decomposed into spectra.

Video on the topic

Quadrangular pyramid is a pentahedron with a quadrangular base and a side surface of four triangular faces. The lateral edges of the polyhedron intersect at one point - the vertex of the pyramid.

Instructions

A quadrangular pyramid can be regular, rectangular or arbitrary. Correct pyramid has a regular quadrangle at its base, and its vertex is projected into the center of the base. The distance from the top of the pyramid to its base is called the height of the pyramid. Side faces are isosceles triangles, and all edges are equal.

The base of a regular one can be a square or a rectangle. The height H of such a pyramid is projected to the point of intersection of the diagonals of the base. In a square and a rectangle, the diagonals d are the same. All lateral ribs L pyramid with square or rectangular base are equal to each other.

To find the edge of a pyramid, consider right triangle with sides: hypotenuse - the desired edge L, legs - the height of the pyramid H and half the diagonal of the base d. Calculate the edge using the Pythagorean theorem: square of the hypotenuse equal to the sum squares of legs: L²=H²+(d/2)². In a pyramid with a rhombus or parallelogram at the base, the opposite edges are equal in pairs and are determined by the formulas: L₁²=H²+(d₁/2)² and L₂²=H²+(d₂/2)², where d₁ and d₂ are the diagonals of the base.