Begin to speak about the area of a rectangle in elementary grades. There are various formulas by means of which it is possible to calculate it. Let's consider some of them.
It is required to you
- - ruler;
- - pencil;
- - calculator.
Instruction
1. The rectangle is a quadrangle at which all corners are equal to 90 degrees. Its sizes are defined by length of the parties. It has a number of properties: - the opposite parties are equal and parallel; - diagonals are equal and are halved in a point of intersection; - it can be divided into two equal rectangular triangles; - around a rectangle it is possible to describe a circle, its diameter is equal to length of its diagonal.
2. The area of a rectangle represents the work of the parties belonging to one corner. It is designated by Latin letter S. If there is some rectangle which has a – length, and b – width, a formula of the area has an appearance: S = a×b. It is the most widespread and elementary formula.
3. It is possible to find the area if there are data on its perimeter. The perimeter of a rectangle is equal to the sum of its parties (a+b) increased by two :P = ×2. If in a task it is known and one party, then it is necessary to use the following formula: S = a×((P-2a)/2)
4. It is also possible to use calculation of the area of a rectangular triangle. It is equal to the work of a half of its legs. The hypotenuse will represent rectangle diagonal, and legs will be the parties. To find its area, it is necessary to increase the received value by two. Such option suits those who know how to find the area of a triangle.
5. For finding of the area also trigonometrical functions can be used. Diagonal can be found on a formula: d = √ (a2 + b2). Corners between diagonals are as follows: α = 2arctg (a/b), β = 2arctg (b/a), α + β = 180 °. If length of diagonals and a corner between them is known, the area is on a formula: S = d2 • sin(α/2) • cos(α/2).
6. If the rectangle is inscribed in a circle, its diagonal will be equal to the radius of this circle. And the area can be found as follows: S = a× √ (R^2-a^2).
7. The quadrangle at which all parties are equal is called a square. Its area is equal to length of its parties in a square. Still it can be found as the square of its diagonal divided into two.