Advice 1: How to find the side of a quadrilateral

A quadrilateral has four sides, which can be found using parameters such as angle, area, diagonal. The problem of finding the area of a quadrilateral are often found in the geometry course.
How to find the side of a quadrilateral
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.
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
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.
How to find the side of a quadrilateral

Advice 2: 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.
How to find angle of a rhombus
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.
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