Instruction

1

The simplest variant of a quadrilateral is called a rectangle. It has four sides, with parallel sides equal to each other. Perpendicular to each other sides form an angle equal to 90 degrees. One of these sides is called the length and the other perpendicular to it width. By multiplying the length by the width to calculate the area of a rectangle. From this we can conclude that the side of the rectangle, for example, the width a may be found by dividing the square length:

a=S/b.

If the problem you are given a square, then direction can be found by the formula:

a=√S, as the sides of the square are equal.

a=S/b.

If the problem you are given a square, then direction can be found by the formula:

a=√S, as the sides of the square are equal.

2

The area of a parallelogram to find some more difficult than the same parameter of the rectangle. For example, draw a parallelogram with sides a and b and the angle α. If the height and area of a parallelogram, find the direction according to the following formula:

a=S/h, where h is the height of a parallelogram, S - area of a parallelogram

If the objective of this side and the angle α and the area of a parallelogram, the formula will change as follows:

a=S/b*sinα

A rhombus is an equilateral parallelogram, so the formula for finding the area of a rhombus is written in the following form:

S=a^2*sinα

Hence, side of a rhombus is:

a=√S/sinα

a=S/h, where h is the height of a parallelogram, S - area of a parallelogram

If the objective of this side and the angle α and the area of a parallelogram, the formula will change as follows:

a=S/b*sinα

A rhombus is an equilateral parallelogram, so the formula for finding the area of a rhombus is written in the following form:

S=a^2*sinα

Hence, side of a rhombus is:

a=√S/sinα

3

Another kind of quadrilateral - trapezium. She also has four sides, but they are not always equal. The trapezoid of the first two sides is the base and the rest of the side. Draw an isosceles trapezoid with two sides - bases and the angle α at the base. The figure shows that when holding perpendicular to the base forms a right triangle. If you hold the two projections, we obtain two right triangles, which are equal. Find the smaller leg of the triangle by subtracting the lengths of the bases. Then, knowing the angle, find the side of the trapezoid.

# Advice 2: How to calculate the sides of a quadrilateral

A quadrilateral can be right or have an arbitrary shape. For the correct figures known relations between the elements. These relationships are expressed by formulas allowing to find

**the parties**through other options.Instruction

1

To the right

**of the quadrilaterals**are the parallelogram and the trapezoid. If all**sides**of parallelogram are equal, such a figure is called a rhombus. If you have a parallelogram, all four corners are straight, then it is a rectangle. A special case of a rectangle — a square.2

For example, a given quadrilateral is a square. If you know its perimeter, the side is equal to one-fourth of the perimeter. To calculate

**side**of a square in his square, you need to take the square root of the number of equal size. If you know the diagonal, to find**the parties**divide the diagonal by the square root of the number two.3

If you want to define

**the sides**of a rectangle or parallelogram, is insufficient to know only the perimeter or the area. You must additionally know the relationship between the parties. Let us denote one side of the parallelogram (rectangle) N, then the other party kN. If the value k is known,**the sides**can be calculated via the perimeter P according to the formula N= R/2(1+k) or using the area S by the formula N=√(S/k).4

The parallelogram

**sides**can be calculated, if other than area and perimeter of a figure is set to the angle ά between the parties. Finding one side of a parallelogram is reduced to the solution of the quadratic equation:N2-NхP/2+S=0где the N — side of the parallelogram P is the perimeter of a parallelogram S is the area of a parallelogram.The second side of a parallelogram find M from formulas square S=NхMхSinά5

To find

**side**of a trapezoid is also possible in a known area and perimeter of a figure when you set the angle between the base of the trapezoid and the lateral side.6

To find the sides of an arbitrary quadrilateral split figure auxiliary line into two triangles. Apply the known formulas of the ratio of triangle elements. For a possible solution of the problem must be known not only the area and perimeter of shapes, but the angles of the quadrilateral.

# Advice 3: How to find angle of a rhombus

Diamond formed from a square when stretching shapes for the peaks situated on the same diagonal. Two angles be less direct. The other two angle increases, becoming stupid.

Instruction

1

The sum of the four interior angles of a rhombus is equal to 360°, as in any quadrilateral. Opposite angles of a rhombus are equal, it is always one pair of equal angles — angles sharp, the other blunt. Two angles adjacent to the same side sum to a straight angle. Diamonds with the same size hand, may appear very different from each other. This difference is due to different values of internal angles. Therefore, to find the angle of a rhombus is not enough to know only his side.

2

Sufficient to determine the angles of a rhombus is the knowledge of the diagonals of the figure. After conducting the rhombus , both diagonals rhombus is divided into four triangles. The diagonals of a rhombus are located at a right angle, consequently, the resulting triangles are rectangular. Rhombus — symmetrical shape, its diagonals are both axes of symmetry, so all the internal triangles are equal. The sharp corners of the triangles formed by the diagonals of a rhombus is equal to half the angles of the rhombus that you need to find.

3

The tangent of an acute angle of a right triangle is the ratio of the sides opposite to the surrounding. Half of each diagonal of a rhombus is the leg of a right triangle. If the large and small diagonals of a rhombus to identify d₁ and d₂, respectively, and the angles of a rhombus — A (sharp) and (blunt), then the ratio of sides in right triangles inside the rhombus follows: tg (A/2)=(d₂/2)/(d₁/2)=d₂/d₁, tg(B/2)=(d₁/2)/(d₂/2)=d₁/d₂.

4

According to the formula of double angle tg (2α) = 2/(сtg α tg α) find the tangents of the angles of a rhombus: tg A = 2/((d₁/d₂)-(d₂/d₁)) and tan B =2/((d₂/d₁) to(d₁/d₂)). On trigonometric tables, find the angles corresponding to the calculated values of their tangents.