Calculation of the perimeter of the square is an important skill. And it is not only about school classes. After all, with the help of simple mathematical actions, you can easily calculate the number of desired building materials. For example, to install a fence around the perimeter of a square section or shook wallpapers in a square room.
To find the perimeter of the square, you need to know the value of one of the parties, the area is either the radius of the circle described. Consider these methods in more detail.
How to find the perimeter of the square, if one side of the square is given
- The perimeter of the figure is the sum of all of its sides. Since the square is only 4 sides, its perimeter is equal to:
P \u003d a + in + c + d,
where p is the perimeter
A, B, C, D - sides. - Knowing that the square of all parties are equal, simplify the formula:
P \u003d 4a,
Where is one of the parties,
4 - the sum of the parties. - Example Solution: If the side is 7, then
P \u003d 4 * 7 \u003d 28.
How to find the perimeter of the square if the square square is given
- The square square is calculated by the formula:
S \u003d a * aq \u003d a ²
where S is the area,
A - any side. - We rewrite the formula:
a² \u003d s,
A \u003d √s.
Example Solution: If the area is 121, then
A \u003d √121 \u003d 11. - Knowing the side of the square, we can find the perimeter:
P \u003d 4 * a. - An example of a solution: p \u003d 4 * 11 \u003d 44.
How to find the perimeter of the square if the radius of the circle described
Suppose we are given a square and knows the radius of the circle describing it from all sides. If you hold a diagonal between opposite square angles, we will get 2 triangles with straight corners. In this case, the sin does not take advantage of the Pythagora theorem, which says: "The sum of the squares of the length of the cathets is equal to the square of the length of the hypotenuse."
What else we know:
- The parties B and C in 2-triangles are equal, since it is the sides of the square. They are cathets.
- Triangles have overall hypotenuse A, which is also a circle diameter.
- The diameter is equal to two radius (2r).
We will proceed to find the perimeter:
- According to Pythagore's theorem:
c² + c² \u003d a ²
where in and s - the catts of the rectangular triangle,
A - hypotenuse. - Knowing that A (hypotenuse) \u003d 2R, and B \u003d C, simplifies the formula:
in + c² \u003d (2r) ²,
2v² \u003d 4 (R) ², reduce 2:
in \u003d 2 (r) ²,
B \u003d √2r, where
B - side of the square. - Since the perimeter of the square is equal to the sum of the parties, we have modified the formula:
P \u003d 4√2r,
where p is the desired perimeter
4 - the sum of the parties,
√2r - side length. - We simplify the formula:
P \u003d 4√2 * 4√r,
P \u003d 5,657r,
where p is the desired perimeter
R is a circle radius.
Example Solution:
If the circle radius is 20:
P \u003d 5,657 * 20 \u003d 113.14.
The numbers are quickly forgotten, but the task can always be solved using the Pythagores theorem:
in + c² \u003d (2 * 20) ²,
2v² \u003d 40²,
2v² \u003d 1600, divide by 2:
c² \u003d 800,
B \u003d √800,
\u003d 28,28,
Where B is one side.
So,
P \u003d 4 * 28,29,
F \u003d 113.14.
Ways to find the perimeter of the square are many, but they all boil down to the fact that the perimeter is equal to the sum of all the parties.
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