Advice 1: How to find the sides if the perimeter is known

The perimeter of a plane figure is the sum of the lengths of all its sides. But to find the sides of the figure, knowing only the perimeter is not always feasible task. Often, more data are needed.
How to find the sides if the perimeter is known
Instruction
1
For square or rhombus task is to find side of the perimeter is solved very simply. It is known that these two shapes with 4 sides and all of them are equal, so the perimeter p of a square and a rhombus is 4a, where a is the side of the square or rhombus. Then the length of side equal to one-fourth of the perimeter: a = p/4.
2
Easy to solve this problem for an equilateral triangle. He's got three equal length sides, so the perimeter p of an equilateral triangle is equal to 3a. Then the side of an equilateral triangle a = p/3.
3
For the rest of the figures need additional information. For example, you may find the sides of a rectangle, knowing its perimeter and area. Suppose that the length of the two opposite sides of the rectangle equal a, and the length of other two sides is b. Then the perimeter p of a rectangle is 2(a+b), and the area s is equal to ab. Get a system of equations with two unknowns:
p = 2(a+b)
s = ab.Express from the first equation: a = p/2 - b. Substitute into the second equation and find b s = pb/2 - b2. The discriminant of this equation D = p2/4 - 4s. Then b = (p/2±D^1/2)/2. Discard the root that is less than zero, and substitute in the expression for side a.

Advice 2: How to find the sides of the rectangle

A special case of a parallelogram - rectangle – only known in Euclidean geometry. Have a rectangle all the angles are equal, and each of them individually is 90 degrees. On the basis of private properties of the rectangleand from the properties of the parallelogram of the parallel opposite sides can find a hand figure by the given diagonals and angle from their intersection. Calculating sides of a rectangle based on additional constructions and apply the properties of the resultant shapes.
How to find the sides of the rectangle
Instruction
1
Draw a rectangle EFGH. Record the known data: the diagonal of the rectangle EG, and the angle α, obtained from the intersection of the two equal diagonals FH and EG. Build the figure and mark the diagonal between them the angle α.
How to find <b>hand</b> <strong>rectangle</strong>
2
The letter And mark the point of intersection of the diagonals. Consider the constructions formed by the triangle EFА. According to the property of the rectangle, its diagonals are equal and are bisected by the intersection point A. Calculate the values of FA and EA. Since the triangle is isosceles EFА and his side of EA and FA are equal and accordingly equal to half the diagonal EG.
3
Next, calculate the first side EF of the rectangle. This is the third unknown side of the considered triangle EFА. According to the theorem of the cosines of the appropriate formula, find the side EF. To do this, substitute in the formula for cosines of the previously obtained values of FA equal to the sides EA and the cosine of the known angle α between them. Calculate and record the obtained value of EF.
How to find <b>hand</b> <strong>rectangle</strong>
4
Find the second side of the rectangle FG. For this we consider another triangle EFG. It is rectangular, where the hypotenuse BC and the side EF. According to the Pythagorean theorem, find the second leg FG with the applicable formula.
How to find <b>hand</b> <strong>rectangle</strong>
5
In accordance with the properties of the rectangle, its opposite edges are equal. Thus, the side GH is equal to the side EF, and = FG. Write in the answer all the computed sides of the rectangle.

Advice 3: How to find the area and perimeter of a square

A square is a geometrical figure consisting of four sides of equal length and four right angles, each of which is equal to 90°. Determine the area or perimeter of a quadrilateral, with anyone, is required not only when solving problems in geometry and in everyday life. These skills can be useful, for example, during repairs when calculating the right amount of materials - floor coverings, walls or ceiling, as well as a breakdown of lawns and garden beds etc.
How to find the area and perimeter of a square
Instruction
1
To find the area of a square multiply the length value by the value of width. As the square length and width are the same, then the value enough to square. Thus, the area of a square equals length of its side squared. A unit of area can be square millimeters, centimeters, decimeters, meters, kilometers.To determine the area of a square, you can use formulas = aa, where S is the area of a square and the side of the square.
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Example No. 1. The room is square-shaped. How much plastic (in square metres) will be required in order to completely cover the floor, if the length of one side of the room is 5 meters.Write down the formula: S = aa. Substitute it specified in the condition data.Since a = 5 m, hence the area will be Ravna (room) = 5x5= 25 sq m, so and S (laminate) = 25 sq. m.
3
The perimeter is the total length of the border. Squared perimeter is the length of all four, with the same sides. That is, the perimeter of the square is the sum of all its four sides. To calculate the perimeter of a square, it is sufficient to know the length of one side. Perimeter is measured in millimeters, centimeters, decimeters, meters, kilometers.To define a perimeter formula:P = a + a + a + a Ilir = 4a, gder perimeter,and side length.
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Example No. 2. For finishing works of the premises in the form of a square required ceiling moldings. Calculate the total length (perimeter) skirting, if the value of one side of the room is 6 meters. Write down the formula P = 4a.Substitute it specified in the condition data:P (room) = 4 x 6 = 24 meters.Consequently, the length of the ceiling moldings will also be equal to 24 meters.
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