Instruction

For square the perimeter (P) is equal to four times the value of one of its sides (b). P = 4*b or the sum of the lengths of all its sides P = b + b + b + b. Square square expressed as the product of two adjacent sides. Find the length of one of the sides square. If you only know the area (S), take its square root a = √S. Next, determine the perimeter.

Given: area square equal to 36 cm². Find the perimeter of the figure. Solution 1. Find the side square: b = √S, b = √36 cm², b = 6 cm. Find the perimeter: P = 4*b, P = 4*6cm, P = 24 cm. Or P = 6 + 6 + 6 + 6, P = 24cm Answer: perimeter square area 36 cm² is equal to 24 cm.

Find the perimeter square through the area is possible without resorting to an extra action (calculating the side). To do this, use the formula for calculating the perimeter, which is valid only for square P = 4*√S.

Solution 2: Find the perimeter square: P = 4*√S, P = 4*√36cm², P = 24 cm Answer: perimeter square equal to 24 cm.

Many parameters of this geometric figure are interconnected. Knowing one of them, you can find any other. There are also the following calculation formulas: Diagonal: a² = 2*b², where a is the diagonal, b is the side square. Or a²=2S. Radius of the inscribed circle: r = b/2, where b is the side. Radius of the circumscribed circle: R = ½*d, where d is the diagonal square.Diameter of the circumscribed circle: D = f, where f is the diagonal.

Perimeter is the total length of the sides of the geometric figure. But if there is a need to quickly calculate the perimeter of something (for example, during repairs or construction), not everyone can do it with ease. Recall the basic rules for calculating the perimeter.

You will need

• geometric figure, ruler, pen

Instruction

Perimeter for squares and rhombuses, it is calculated by the formula P \u003d 4a, where a is the length of one side of the figure. Since all its sides are equal, measure one side and multiply the resulting number by the number of sides, i.e. for four.

For rectangles and parallelograms, because they have not all sides equal, but only opposite ones, there is another formula: P \u003d 2 (a + b). By a and b are meant adjacent sides. Multiply their total length by two.

To get the perimeter of a trapezoid, sum the lengths of all its sides (they are not the same for a trapezoid), i.e. in this case, use the formula P=a+b+c+d.

The general formula for calculating the perimeter of a triangle looks like P \u003d a + b + c, i.e. you will have to add the lengths of the sides of the triangle. But since there are different types of triangles, the calculations can be done differently. For example, if you know that the triangle you are measuring is equilateral, then multiply the length of its side by three.

It is more difficult to calculate the perimeter of a circle (circumference, p). It is known that the circumference is 317 times the diameter of the circle (d). IN mathematics this ratio is usually denoted by the letter "Pi" (?) and is averaged as 3.14. It turns out that pd=?. Hence p=?d=2?r, where r is the radius of the existing circle. Therefore, to calculate the perimeter of a circle, you first need to find the radius of the circle and then multiply that number by 2 times 3.14.

If you need to know the perimeter of the arc, then first you need to measure two quantities - the length of the radius of the arc and the central one, i.e. formed by two radii (in degrees, n). Substitute the obtained values ​​into the formula p=Prn180°.

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Tip 3: How to find the side of a square if its diagonal is known

A square is one of the simplest geometric shapes in terms of calculating its parameters - the lengths of the sides and diagonals, area and perimeter. This is determined by the fact that, unlike other polygons, the values ​​​​of all its angles are always known, and it is also enough to know the length of just one side. Finding the length of a side square along the known length of the diagonal, both in general terms and with practical calculations, is not difficult.

Instruction

Use the Pythagorean theorem, the algebraic formulation of which states that in a right triangle the sum of the squares of the lengths of the legs is equal to the square of the length of the hypotenuse: a² + b² = c². Since the diagonals square divide it into two just such right-angled triangles, in which, moreover, the lengths of the legs are the same, then we can formulate such a property square, as a geometric figure: the square of the length of the diagonal is equal to twice the square of the length of the side (2a²=c²). From this it follows that the length of the side is equal to the square root of half square diagonal length: a=√(c²/2).

Use the calculator built into the Google search engine for practical calculations for calculating the length of a side square. For example, if the known length of the diagonal is 15 centimeters, then going to the search engine website, enter the following query: "the root of ((15 squared) / 2)". If you're used to using the ^ symbol to represent exponentiation and sqrt to represent square root, then Google will correctly understand this query: "sqrt (15^2/2)". In any case, the answer will be the same: the length of the side square equals 10.6066017 centimeters.

Use, for example, a software calculator from the standard set of Windows operating system programs as an alternative way to calculate the length of a side square. The link to launch it is hidden quite deep in the main menu of the system - after clicking on the "Start" button, you need to open the "All Programs" section, go to the "Standard" subsection, click on the "Utilities" section and select "Calculator". A faster way is to press the keyboard shortcut WIN + R, type the command calc and press the Enter key.