Instruction

1

The concept of quadrilateral is the General name for several geometric shapes. Is a parallelogram, rectangle, square, rhombus and trapezoid. Some of them are special cases of other, respectively, the formula areas are derived from one another by different simplifications.

2

To calculate

**area**of arbitrary**quadrilateral**can be, regardless of its variants. It is enough to know the lengths of the diagonals, of which he has two, and the value of the angle between them:S = 1/2•d1•d2•sin α.3

Feature parallelogram – pairwise equality and parallelism of the opposite sides. There are several formulas for finding its area: the product of its side on height spent to it, and the result of the multiplication of the lengths of two adjacent sides the sine of the angle between them:S = a•H;S = AB•BC•sin ABC.

4

Rectangle, rhombus, square – all are special cases of a parallelogram. The rectangle of each of the four corners is 90° rhombus implies the equality of all sides and perpendicular diagonals, a square has the properties of both of them, i.e. all its angles are straight, and the sides are equal.

5

Based on these features, the area of each of these shapes are determined by the formulas:PM = a•b – side b is at the same time and height;AB = 1/2•d1•d2 is a consequence of the General formula the product of the diagonals simplification sin 90° = 1;CV = a2 – side are equal and are both heights.

6

Trapezoid different from other quadrilaterals that only two of its opposite sides parallel. However, they are not equal, and the other two sides not parallel to each other. Area of a trapezoid equals half-sum of bases (parallel sides, usually the horizontal) to a height (a vertical line connecting both bases):S = (a + b)•h/2.

7

In addition,

**the area**of a trapezoid can be calculated if you know all the lengths of the sides. This rather cumbersome formula:S = ((a + b)/2)•√(c2 - (((b - a)2 + c2 - d2)/(2•(b - a)))2), c and d – sides.