Draw a box using the pencil and ruler, placing the base horizontally. This is a classic form of representation of shapes, which can be used to demonstrate all the conditions of the problem. Then to solve it will be much easier.
Look at the picture. Have a box of six pairs of parallel faces. Each pair represents an equal two-dimensional shapes, which in General case are parallelograms. Accordingly, their areas are also equal. Thus, the total surface is the sum of the three matching variables: square of the top or bottom of the base, the front or rear faces, right, or left face.
To find the square faces of a parallelepiped, we need to consider it as a separate figure with two dimensions, length and width. At the well-known formula area of a parallelogram equals the base to the height.
The direct box only the bases are parallelograms, all the lateral faces are rectangular in shape. The area of this figure is obtained by multiplying the length by the width, since it coincides with the height. In addition, there exists a rectangular parallelepiped, all faces of which – rectangles.
The cube is also a parallelepiped, which has the unique property – equality of all measurements and the numerical characteristics of the faces. The area of each of its sides are equal to the squared length of any edge, and the full surface is obtained by multiplying this value by 6.
The form of a parallelepiped with square corners can often be found in everyday life, for example, in the construction of houses, construction of items of furniture, household appliances, toys, stationery, etc.
Example: find the area of each lateral face direct of the box, if you know that the height is 3 cm, the perimeter of the base is 24 cm and base length greater than width 2 cm Solution.Write down the formula for perimeter of parallelogram P = 2•a + 2•b. The statement b = a + 2 therefore P = 4•a + 4 = 24, whence a = 5, b = 7.
Find the area of the lateral faces of the figure with 5 sides and 3 cm rectangle:Ѕб1 = 5•3 = 15 (cm2).The area of parallel side faces, by definition of the box, also equal to 15 cm2. It remains to determine the area of the other pairs of sides with the sides 7 and 3:Ѕб2 = 3•7 = 21 (cm2).
Advice 2: How to determine the surface area
As in mathematics lessons and in various practical matters regularly faced with the need to find the area of a particular surface. It is necessary to calculate the amount of materials for construction, the layout of the land, in the manufacture of parts on the machine. The ability to solve geometrical tasks of the school in this case be very useful.
You will need
- - a geometric solid with specified parameters;
- and measuring devices;
- formula to calculate area of geometric shapes.
If you want to calculate the surface area of the rectangular floor of a room or of a rectangular plot of land, measure their length and width. The results multiply. In this case, the surface area is calculated by the formula S=ab, where S is the surface area, a and b are the sides of the rectangle. The formula for the area of a square would look like S=a2.
If the planar surface has a more complex form, it must be divided into more simple parts of formulas for calculating the area of which you are aware. For example, irregular polygon can be divided into several triangles or triangles and a rectangle. In this case, consider the given in terms of the problem parameters of the polygon.
If you are not dealing with plane figures and geometric bodies need to operate exactly the same. In terms of tasks usually set the parameters of the figure to be built or to calculate. Please read carefully, what kind of area you need to find. Almost every geometrical body has the total surface area, lateral surface area and area of one or two bases.
Calculate the area of the grounds. The cone and pyramid base one. The base of the pyramid is a polygon and is calculated by relevant formula. The square base of a regular quadrangular pyramid calculate by formula the area of a square, that is elevating to the square the length of one of its sides. If the base of the pyramid lies a complex polygon, divide it into more simple with the known parameters. At the base of the cone is the circle, and accordingly, the area is calculated by the formula S=πR2.
Find the lateral surface area. At cuboid it is calculated according to the formula S=p*h, where p is the perimeter of the rectangle of the base and h is the height. The surface area of a cube is calculated by the formula S=4a2, since the lateral surface consists of 4 squares.
For the calculation of the conical surface is most convenient to do a scan. Find the length of a circle given its radius. It will be equal to the arc length of the lateral surface of the cone. The length of an arc calculate the Central angle, then the radius of the circle sector which is the lateral surface of the cone. Knowing these values, find the area of a sector, that is, the lateral surface area of a cone.
To determine the full surface or other geometric bodies add together the square of the lateral surface and bases.
In order to more clearly imagine, what you have to calculate, very easy to use scans.