How To Find The Sum Of The Lengths Of All Edges Of The Box | The Science

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How to find the sum of the lengths of all edges of the box

Are you having difficulty in solving geometrical problem connected with parallelepiped. The principles of solving such problems, based on the properties of the box, presented in a simple and accessible way. Understand - means to solve. Similar problems will no longer cause you difficulties.

Instruction how to find the sum of the lengths of all edges of the box

Step 1:

For convenience, we introduce the notation A and B sides of the base of the box; C - side of his face.

Step 2:

Thus, the base is parallelepiped parallelogram with sides A and B. The parallelogram - a quadrilateral, opposite sides of which are equal and parallel. From this definition, it follows that the anti-side A is equal to her side A. Since the opposing face of the box are (from the definition), the top of its faces, too, has two sides equal A. Thus, the sum of all these four sides equal to 4A.

Step 3:

The same can be said about the B side opposite to her side at the base of the box is equal to B. The top (opposite to) face of the box also has two sides equal B. The sum of all these four sides equal 4B.

Step 4:

The side face of the box are also parallelograms (derived from the properties of the box). Rib With both a party to two adjacent faces of the box. As the face of the box opposite pairs are equal, then all of its lateral edges are equal and are equal to C. The amount of the lateral edges - 4C.

Step 5:

Thus, the sum of all edges of the box: 4A + 4B + 4C or 4 (A + B + C) A special case of a direct parallelepiped - a cube. The sum of all of its edges equal to 12A. Thus, the solution of the problem with respect to the spatial body can always be reduced to problems with plane figures for which this body is broken.