How to find the area of diagonal section of a prism

How to find the area of diagonal section of a prism

The prism is a polyhedron with two parallel bases and side sides in the form of a parallelogram and in the quantity equal to number of the parties of a polygon of the basis.


1. In any prism the side edges are located at an angle to the basis plane. A special case is the direct prism. In it sides lie in the planes perpendicular to the bases. In a direct prism the side sides are rectangles, and side edges are equal to prism height.

2. Diagonal section of a prism — the part of the plane which is completely concluded in internal space of a polyhedron. Diagonal section can be limited to two side edges of a solid and diagonals of the bases. It is obvious that the number of possible diagonal sections at the same time is defined by the number of diagonals in a basis polygon.

3. Or as borders of diagonal section diagonals of side sides and the opposite sides of the bases of a prism can serve. Diagonal section of a rectangular prism has the rectangle form. Generally any prism a form of diagonal section - a parallelogram.

4. In a rectangular prism the area of diagonal section S is determined by formulas: S=d*Hgde d is the diagonal of the basis, H is prism height. Or S=a*Dgde and — the party of the basis belonging at the same time to the section plane, D — the diagonal of a side side.

5. In any indirect prism diagonal section — a parallelogram which one party is equal to a side edge of a prism, another - basis diagonals. Or diagonals of side sides and the party of the bases between prism tops from where diagonals of side surfaces are carried out can be the parties of diagonal section. The area of a parallelogram of S is defined by a formula: S=d*hgde d is the diagonal of the basis of a prism, h — parallelogram height — the diagonal section of a prism. Or S=a*hgde and — the party of the basis of a prism which is and border of diagonal section, h — parallelogram height.

6. For determination of height of diagonal section it is not enough to know the linear sizes of a prism. The grounds given about a prism inclination to the plane are necessary. The further task comes down to the consecutive solution of several triangles depending on basic data about corners between prism elements.

Author: «MirrorInfo» Dream Team