Advice 1: How to find the area of the diagonal cross section of the prism

Prism — a polyhedron with two parallel bases and lateral faces in the shape of a parallelogram and in an amount equal to the number of sides of the base polygon.
In any prism the lateral edges are at an angle to the plane of the base. A special case is a straight prism. Her sides lie in planes perpendicular to the bases. In straight prism lateral faces rectangles and the side edges equal to the height of the prism.
The diagonal section of the prism — part of the plane completely enclosed in the inner space of the polyhedron. Diagonal cross section can be limited by two side edges and a geometric body diagonals of the bases. It is obvious that the number of possible diagonal sections is determined by the number of diagonals in a polygon base.
Or borders of a diagonal cross-section can serve as the diagonal side faces and the opposite side of the bases of the prism. Diagonal cross section of a rectangular prism is a rectangle. In the General case of an arbitrary prism form a diagonal of the cross section is a parallelogram.
In a rectangular prism of square cross-section diagonal of S is defined by the formula:
where d is the diagonal of the base,
H — the height of the prism.
Or S=a*D
where a — side of the base, at the same time belonging to the cutting plane
D — the diagonal of the side face.
In the random indirect prism diagonal cross section is a parallelogram, one side of which is equal to a lateral edge of the prism, the other diagonal of the base. Or sides, diagonal lines can be diagonal side faces and the sides of the bases between the vertices of the prism, where the drawn diagonal side surfaces. The area of a parallelogram S is determined by the formula:
where d is the diagonal of the base of the prism,
h — the height of a parallelogram — diagonal cross-section of the prism.
Or S=a*h
where a — side of the base of the prism, which is the border of the diagonal lines,
h — the height of the parallelogram.
To determine the height of the diagonal section is not enough to know the linear dimensions of the prism. The necessary data about the inclination of the prism to the plane of the base. A further problem is reduced to the consecutive solution of several triangles depending on the source of data on the angles between the elements of prism.

Advice 2: How to find the cross-sectional area of the prism

A prism is a polyhedron, the base of which are equal polygons, lateral faces parallelograms. To find the cross-sectional area of the prism, you must know what the section is considered in the job. Distinguish between perpendicular and diagonal cross-section.
The method of calculating cross-sectional area also depends on data that is already available in the problem. In addition, the decision is determined by what lies at the base of the prism. If you want to find the diagonal section of a prism, find the length of the diagonal, which is equal to the root (the base of the sides in the square). For example, if the base of the sides of a rectangle is 3 cm and 4 cm, respectively, the length of the diagonal is the square root of (4x4+3x3)= 5 cm Area of diagonal lines will find by the formula: diagonal of the base times the height.
If the base of the prism is a triangle to calculate the cross-sectional area of the prism use the formula: 1/2 of the base of the triangle multiplied by the height.
If the base is round, the cross-sectional area of a prism find the multiplication of the number "PI" in the radius of a given shape on the square.
The following types of prisms — right and straight. If you want to find the right section of the prism, you need to know the length of one side of the polygon, because the base has a square whose all sides are equal. Find the diagonal of a square which equals to the square root of two. Then multiplying the diagonal and the height, you will get a cross-sectional area of the right prism.
Prism has its own properties. So, the area of the lateral surface of any prism is calculated by the formula where is the perimeter of the cross section perpendicular to the length of a side edge. In this perpendicular cross-section perpendicular to all the lateral edges of the prism, and its corners are line angles of the dihedral angles at the respective side edges. Perpendicular cross-section perpendicular to all the lateral faces.
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