obtain the relation i+e = n+dalita for a
prism formula
Soluções para a tarefa
Resposta:
The area of the prism can be obtained by adding its lateral area with the areas of the bases. The process of calculating these areas ends up being facilitated because the two bases of a prism are the same, therefore, it is enough to calculate the area of a base and multiply the result by 2. A lateral area of the prism is given by the sum of the areas of the lateral faces , which also tend to be the same or follow a pattern. Of course, this does not eliminate the fact that, in some cases, there are prisms that will require separate calculation for each of their faces, but these cases are more rare.
In this article we will discuss some examples of calculating the area of prisms. The full text of this calculation can be found here.
Example 01
(UNESP / 2016) A straight-to-rectangle parallelepiped was divided into two prisms by a plane that contains the diagonals of two opposite faces, as shown in the figure.
Comparing the total amount of paint needed to paint the external faces of the cobblestone before the division with the total amount needed to paint the external faces of the two prisms obtained after the division, there was an approximate increase of
a) 42%.
b) 36%.
c) 32%.
d) 26%.
e) 28%.
Solution:
We first calculate the area of the straight-rectangle prism. Note that it consists of two rectangular side faces of base 3 and height 1, two side faces of base 4 and height 1 and two rectangular bases of length 4 and width 3.
A side area is equal to the sum of the areas of the side faces, and a total area is the sum between this result and an area of the two bases. Observe:
Al = 4 · 1 + 4 · 1 + 3 · 1 + 3 · 1 = 4 + 4 + 3 + 3 = 14 cm2
Ab = 4 · 3 + 4 · 3 = 12 + 12 = 24 cm2
The total area of the straight-rectangle prism is:
Air = 14 + 24 = 38 cm2
Now we will calculate the area of one of the triangular prisms. As they were created by the section on the diagonal bases, they have congruent measures and, therefore, just find an area of one of them and multiply the result by 2. However, we need to find out the length of that diagonal. For this, we will use the Pythagorean theorem. It is only possible to present it because we have a guarantee that the angles between two edges (except as introduced by the cut) are straight, since it is a straight-rectangle prism.
Explicação:
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