Today, few who do not know how to find the area of a square.While there, it was already in the distant yesterday ... That is, in a time when everybody knew how to calculate the area of a square, because today, as if it may sound absurd, such questions are constantly being started appearing on the Internet.It is strange, to say the least - it is terrible.
Back in elementary school are taught how to find the area of a square.But you must first learn to identify the area of a rectangle (a square - still a rectangle, but with equal sides).
proposed to build on a certain square measure measuring areas - square centimeter or square meter.This measure space is a square with a side equal to a one centimeter or one meter.Depending on the size of the area to be measured, it can be hectare (square kilometer), or ar (a square with sides of 100 m, in other words - "weaving").These squares and put thoughts on the measured rectangle.
For the experiment should take a small rectangle with sides, for example, equal to 3 and 5 centimeters.For clarity, the younger students are invited to draw a shape on a sheet in a cage, and then dividing the rectangle parallel lines along the length and width, placing them at a distance of two cells.Presumably, the two cells in the ordinary school notebook correspond to one centimeter.Thus, it appears that the rectangle is divided into square centimeters, that is placed in it square centimeters - Measures area measurement.
next step is to count the squares together into a rectangle with a side of one centimeter.You can count them first in the usual way, pointing to each stick.Then be sure to use an unlearning multiplication table: Get five columns, each with three squares.Multiplying them easy to get 15 square centimeters.In simple terms, the area of any rectangle is multiplying its length and width.
Replacing the number 5 on the "a", and the number 3 on the «b», children are easy to deduce the formula of finding the area of a rectangle.So, it turns out that S = a x b.But it is - a formula for the rectangle.We also want to display a rule, explaining how to find the area of a square!
It's very simple!The parties are at the square, so you can replace the direction of «b» in this formula to "a".Then appears the following expression: S = ax as well.Multiplying a number by itself gets the square of the number or the number in the second degree.
However, there are other ways of finding the area of a square.This, of course, has more math problems.But their decision to appear certain formula.For example, ask to learn how to find the area square not on the side and on the diagonal.
To solve this problem, there is little knowledge of the elementary school.We need the Pythagorean theorem.First we construct a square, for example, NMOP diagonal NO = m.We get the two equal isosceles right triangle with the base m.
Applying the above mentioned theorem, find the side of a right triangle.NM squared + MO = NO squared in the square.But since MO = NM, then we obtain NM NM + squared squared = NO squared.From 2 NM squared = NO squared.Find NM squared can NO dividing the square into two.
NM But in the square - this is just the answer to the question of how to find the area of a square!A NO - is the diagonal of a square.So, we can derive a new formula, which states that the area of the square is equal to half of its diagonals, erected in the second degree.
can derive a formula for finding the area of a square radius of a circle inscribed in it or around it described.But whatever the problem, we did not decide the foundation will forever rule that we learn in elementary school - that multiplying two sides of the rectangle, you can find its area.
