Sometimes a person gets close to the need to find the perimeter of the square.For example, the need to make a fence around a square area, wallpapered square room or arrange mirrors wall square dance hall.To calculate the amount of material required, it is necessary to make special calculations.And it is here that, not knowing how to find the perimeter of the square, it is necessary to acquire the material "by eye".Okay, if it's cheap wallpaper, but the extra mirror which then put?And with a shortage of material then it is quite difficult to find the same quality extra.
So, how do you know what is the perimeter of the square?We know that all parties are equal to the square.And if the perimeter - the sum of all sides of a polygon, the circumference of a square can be written as (q + q + q + q), where q - value indicating the length of one side of a square.Naturally, the most convenient is to use multiplication.Thus, the perimeter of the square - a quadruple value corresponding to the length of its sides or 4q, where q - side.
But if the only known area of the square whose perimeter is necessary to find out - what to do in this case?And everything is very simple!From the well-known figures, which expresses the area of the square, you need to make the square root.Thus it is found value of the square.Now look for the perimeter of the square is necessary for the removal of the above formula.
Another question, if you need to find the perimeter of the square on the diagonal.We should remember the Pythagorean theorem.Consider a square with a diagonal WERT WR.WR square divided into two rectangular isosceles triangle.If you know the length of the diagonal (conditionally accept her for z, a direction - for u), then the value of the square must be sought on the basis of the formula: the square of z is twice the square of u, and therefore we conclude: u is equal to the square root extracted from the half of the square of the hypotenuse.Next is increasing the result by 4 times - that's you and the perimeter of the square!
Find side of the square can be the radius of the circle inscribed in it.After the inscribed circle touches all sides of the square, where it is concluded - the diameter of a circle equal to the length of the square.A diameter - is known to all - twice the radius.
If you know the radius or diameter of the circle described around the square, here we see that all four vertices of the square are placed on the circle.Hence, the diameter of the circle is equal to the length of the diagonal of the square.Taking this situation as a given, followed by calculating the perimeter of the formula for finding the perimeter of its diagonals, discussed above.
Sometimes a problem in which you need to find out what is the perimeter of the square, which is inscribed in an isosceles right triangle so that one corner of the square coincides with the right angle triangle.Known is a leg of the geometric figure.Let the triangle as the WER, where E is the peak of the total.
inscribed square will be marked ETYU.ET side is on the side of WE, EU and the side - side ER.Vertex Y lies on the hypotenuse WR.Considering further drawing, conclusions can be drawn:
- WTY - isosceles triangle, since by hypothesis WER - isosceles, so angle EWR is 45 degrees, and the resulting triangle - square with a corner at the base and 45 degrees, which allows us to assert itisosceles.It follows that the WT = TY.
- TY = ET as the sides of a square.
- Following the same algorithm, we derive the following: YU = UR, and UR = EU.
- Parties triangle can be represented as the sum of the segments.EW = ET + TW, and ER = EU + UR.
- Replacing equal segments, we deduce: EW = ET + TY, and ER = EU + UY.
- If the perimeter of the inscribed square is given by (ET + TY) + (EU + UY), in a different way this can be written, meaning that only the derived values sides of the triangle as EW + ER.That is, the perimeter of a right triangle inscribed in a square with a matching right angle is equal to the sum of the other two sides.
This, of course, not all options for calculating the perimeter of the square, but only the most common.But they are all based on the fact that the perimeter of the quadrilateral - a summarized value of all its sides.And there's no escape!
