Trapeze - a mathematical figure, a quadrangle at which one couple of the opposite parties is parallel and another - is not present. The area of a trapeze - one of the main numerical characteristics.
Instruction
1. The basic formula of calculation of the area of a trapeze looks so: S = ((a + b) *h)/2, where an and b - lengths of the bases of a trapeze, h - height. The bases of a trapeze are called the parties which are parallel each other and are graphically represented parallel to the line of a horizontal. Height of a trapeze is the piece which is carried out from one of tops of the top basis is perpendicular before crossing with the lower basis.
2. There are some more formulas for calculation of the area of a trapeze.S = m*h where m is the average line of a trapeze, h is height. This formula can be brought out of the main as the average line of a trapeze is equal to the half-sum of lengths of the bases and is graphically carried out parallel to them, connecting the middle of sides.
3. The area of a rectangular trapeze of S = ((a + b) *c)/2 - record of a basic formula where instead of height for calculation length of side of c which is perpendicular to the bases is used.
4. There is a formula for determination of the area of a trapeze through lengths of all parties: S = ((a + b)/2) * √ (c^2 - (((b - a) ^2 + c^2 - d^2) / (2 * (b - a))) ^2), where an and b - the bases, c and d - trapeze sides.
5. If on a statement of the problem only lengths of diagonals and a corner between them are given, then it is possible to find the area of a trapeze on the following formula: S = (e*f*sinα)/2, where e and f - lengths of diagonals, and α - a corner between them. Thus it is possible to find not only the area of a trapeze, but also the area of other closed geometrical figure with four corners.
6. Let's assume that r radius circle is entered in an isosceles trapeze. Then the area of a trapeze can be found if the corner at the basis is known: S = (4*r^2)/sinα.Например if the corner is equal 30 °, then S = 8*r^2.