To calculate the area and perimeter of the square, you need to understand the concepts of these values. The square is a rectangle with only four identical sides that have an angle of 90 °. Perimeter is the sum of the lengths of all sides. The area is the product of the length of the rectangular figure on its width.
Square square and how to find it
As mentioned above, the square is a rectangle that has 4 equal sides, so the answer to the question: "How to find the square of the square" is the formula: S \u003d A * A or S \u003d A2 where a is the side of the square. Based on this formula, the side of the square is easily located, if the area is known. To do this, you need to remove the square from the specified value.
For example, S \u003d 121, therefore, A \u003d √121 \u003d 11. If there is no specified value in the square table, you can use the calculator: S \u003d 94, A \u003d √94 \u003d 9.7.
How to find a square perimeter
The perimeter of the square is located according to a light formula: P \u003d 4A, where a is the side of the square.
Example:
- square side \u003d 5, therefore, p \u003d 4 * 5 \u003d 20
- square side \u003d 3, therefore, p \u003d 4 * 3 \u003d 12
But there are such tasks where the area is obviously marked, and you need to find a perimeter. When solving, we need the formulas that are previously represented.
For example: how to find the perimeter of the square, if the area is known equal to 144?
Steps Solutions:
- Find out the length of one side: a \u003d √144 \u003d 12
- Find perimeter: p \u003d 4 * 12 \u003d 48.
Finding the perimeter inscribed square
There are several more ways to find the perimeter of the square. Consider one of them: finding the perimeter through the radius of the circle described. A new term "inscribed square" appears here - this is a square, whose vertices lie on the circle.
Algorithm Solutions:
- since on consideration the square, the formula can be expressed in this way: a2 + a 2 \u003d (2r) 2;
- then the equation should make it easier: 2a2 \u003d 4 (R) 2;
- dELIM EQUATION 2: (A2) \u003d 2 (R) 2;
- remove the root: a \u003d √ (2r).
As a result, we obtain the last formula: A (Side Square) \u003d √ (2r). 
- The found side side is multiplied by 4, then the standard formula for finding the perimeter is applied: p \u003d 4√ (2R).
A task:
Dan Square, which entered the circle, its radius is 5. So, the diagonal of the square is equal to 10. Using the Pythagora theorem: 2 (a2) \u003d 10 2, i.e. 2a 2 \u003d 100. We divide the two and as a result: a2
\u003d 50. Since this is not a table value, we use the calculator: a \u003d √50 \u003d 7.07. We multiply on 4: p \u003d 4 * 7.07 \u003d 28.2. The task is solved! 
Consider another question
Often in the tasks there is another condition: how to find the square of the square if the perimeter is known?
We have already considered all the necessary formulas, therefore, to solve the problems of this type, it is necessary to skillfully apply them and bind together. Let us go right away to the visual example: the square of the square is 25 cm2
, find its perimeter. 
Steps Solutions:
- We find the side of the square: a \u003d √25 \u003d 5.
- We find the perimeter itself: p \u003d 4 * a \u003d 4 * 5 \u003d 20.
Summing up, it is important to recall that such light formulas are applicable not only in training activities, but also everyday life. Perimeter and Square Figure Kids learn to find even in elementary school. In the middle classes a new item appears - geometry, where the Pythagora theorem is at the very beginning of the study. These maths are checked at the end of the school OGE and EGE, so it is important to know these formulas and apply them correctly.
