How To Find The Entire Surface Of The Box | The Science



The Science

How to find the entire surface of the box

To find the full surface of the box, you must sum the area of ​​the lateral surface and two bases. Depending on the shape, the edges may be parallelograms, squares, or rectangles.

How to find the entire surface of the box

Instruction how to find the entire surface of the box

Step 1:

Parallelepiped - a multi-faceted spatial figure consisting of six quadrangles having the shape of a parallelogram. There are direct and oblique parallelepiped. In the first lateral faces are vertical rectangles, they form the second angle with bases other than 90 °.

Step 2:

In this figure, there are two common special cases - square and cube. In all facets of a rectangular parallelepiped - rectangles, cubed - squares. These forms are often found in problem solving to build a three-dimensional projections, determining the length of the vector, drawing graphics molecule chemical formulas and structures, etc.

Step 3:

Based on the foregoing, it can find a complete parallelepiped surface for any its variants. It's enough to sum area of ​​all the faces of the figures: S = 4 + 2 Sbg • • SO.

Step 4:

The first term is called the lateral surface. Consider the side edges, which, according to the property of the parallelepiped are parallel and equal. It parallelograms with sides a, b, or a, b. It is known that the area of ​​the two-dimensional figure is equal to the product of the base and the height: 4 • Sbg = (a + 2 • 2 • a) • h.

Step 5:

It is easily seen that the expression a + 2 • 2 • s - is the base perimeter of the box, thus: 4 • Sbg = Po • h.

Step 6:

So a base area is the product of the horizontal side of the parallelogram to a height ho, carried out by it: So = 2 • a • ho.

Step 7:

Put both values ​​in the general formula: S = P • h + 2 • • with ho.

Step 8:

We direct the box height is the length of the lateral rib: S = P • b + 2 • • with ho.

Step 9:

The same is true for cuboid and base area is twice the product of the lengths of the sides: S = 2 • (a + c) • b + 2 • a • c = 2 • (a • b + b • c + and • to ).

Step 10:

The cube, all measurements are: S = 6 • a².