How to find a square area if the perimeter is known, diagonal? How to find the square of the square inscribed in the circle and described near the circumference: formula, examples of solving problems. How to find the side and diagonal of the square, if its area is known?

Read the article to know how to find the square area in different ways.

Content

A square is an equilateral rectangle. This proper and flat quadrangle has equality in all sides, corners and diagonals. Due to the fact that there is such equality, the formula for calculating the area and other characteristics is slightly modified compared to other mathematical figures. But this does not make tasks too complicated. Let's analyze all the formulas and solutions to this article.

How to find the side of the square, knowing its area?

Square S. Direct and square squares are calculated by the formula: a Multiply by b.. But since the square has a complete equality of the parties, its area will be equal: S \u003d (A) in the second degree.How to find out the size of the side of the square, knowing its area?

If the area of \u200b\u200bthe square square is known, then we find the side by calculating the area from under the square root.
For example, the area of \u200b\u200bthe square is 49, then what is the side equal to?
49 \u003d (a) in the second degree. Solution: a \u003d root of 49 \u003d 7. Answer: 7.

If you need to find the side of the square square, the area of \u200b\u200bwhich is too long, then use the calculator. First dial the number of the area, and then press the root sign on the calculator keyboard. The resulting number will be the answer.

How to find a square diagonal if its area is known?

In this example, we will use the Pythagoras theorem. In a square, all sides are equal, and the diagonal d. We will consider the hypotenuse of a rectangular isosceles triangle with a leg a. Now we find a square diagonal if its area is known:

In order not to paint the entire Pythagorean theorem we will decide on the second option: d \u003d aising, where A is the side of the square.
So, we know the area of \u200b\u200bthe square, for example, it is equal to 64. So one side a \u003d √64 \u003d 8.
It turns out D \u003d 8√2. The root of 2 does not turn out the whole number, so in the answer you can write this way: d \u003d 8√2. But, if you want to calculate the value, then use the calculator: √2 \u003d 1.41421356237 and multiply by 8, it turns out 11, 3137084.

Important: Typically, in mathematics, no numbers with a large number of numbers are left in response. It is necessary to round or leave with the root. Therefore, the answer to the diagonal is if the area is 64 as follows: d \u003d 8√2.

How to find a square area through a diagonal?

The formula for finding the square area through the diagonal is simple:

Now let's write a solution to find the square area through the diagonal:

Diagonal d \u003d 8.
8 in the square is 64.
64 divide by 2 equal 32.
The square area is 32.

Advice: This task has another solution through the Pythagoras theorem, but it is more complex. Therefore, use the solution that we examined.

How to find a square area, knowing its perimeter?

The perimeter of the square square P. - This is the sum of all parties. To find its area, knowing its perimeter, you must first calculate the side of the square square. Solution:

Suppose the perimeter is 24. Divide 24 into 4 sides, it turns out 6 - this is one side.
Now we use the formula for finding the area, knowing what the side of the square square is equal to: S \u003d A in a square, S \u003d 6 in a square \u003d 36.
Answer: 36

As you can see, knowing the perimeter of the square, just find its area.

How to find an area of \u200b\u200ba square inscribed in a circle with a given radius?

Radius R - This is half the diagonal of a square inscribed in a circle. Now we can find a diagonal by the formula: d \u003d 2*R. Next, we find the square of the square inscribed in a circle with a given radius:

The diagonal is 2 multiply by the radius. For example, the radius is 5, then the diagonal is equal 2*5=10.
It was described above how to find the square of the square if the diagonal is known: S \u003d Diagonal in a square divided into 2. S \u003d 10*10 and divide by 2 \u003d 50.
Answer - 50.

This task is a little more complicated, but also easily solved if you know all the formulas.

How to find an area of \u200b\u200ba square described near a circle with a given radius?

The picture shows that the radius of the inscribed circle is equal to half of the side. The side is located according to the reverse formula that depicted in the picture: a \u003d 2*R. Then we find the area of \u200b\u200bthe square described near the circle with a given radius according to the formula S \u003d and in a square. Solution:

Suppose the radius is 7. The side of the square A is 2*7 \u003d 14.
S \u003d 14 in a square \u003d 196.

If you understand the essence of solving such problems, then you can solve them quickly and simply. Let's look at a few more examples.

Examples of solving problems on the topic "Square Square"

To fix the material covered and remember all the formulas, it is necessary to solve several examples of problems on the theme of “square area”. We start with a simple task and move to solving more complex: