Square is called the rectangle with the equal parties. It is, perhaps, the simplest figure in planimetry. Thanks to high degree of symmetry of this figure to calculate the area of a square, only one its characteristic suffices. It can be the party, diagonal, perimeter, radius of the described or inscribed circle.
It is required to you
- calculator or computer
Instruction
1. To calculate the area of a square if length of its party is known, build the party of a square in the second degree (in a square). I.e. use a formula: Pl = C², or Pl = With * With, where: Pl - the area of a square, With – length of its party. The area of a square will be measured in the "square" units of measure of the area corresponding to length of the party. So, for example, if the party of a square is set in mm, cm, inches, dm, m, km, miles, then its area will turn out in mm², cm², inches square, dm², m², km², miles square, respectively. Let, for example, there is a square with the party 10 cm long. It is required to determine its area. Decision: Square 10. 100 will turn out. Answer: 100 cm².
2. To count the area of a square if its perimeter is set, square perimeter and divide into 16. That is use the following formula: Pl = Lane²/16 or Pl = (Lane / 4)², where: Pl – the area of a square, the Lane – its perimeter. This formula follows from previous if to consider that all four parties of a square have equal length. Let there is a square with perimeter of 120 cm. It is required to determine its area. Decision.Pl = (120/4)²=30²=900. Answer: 900 cm².
3. To calculate the area of a square, knowing the radius of the circle entered in it, increase a radius square by 4. In a look the formula this regularity can be written down in the following look: Pl = 4P², a gder – the radius of an inscribed circle. This formula follows from the fact that the radius of the circle entered in a square equals to a half of length of the party of a square (as diameter of such circle is equal to the party of a square). For example, let there is a square with a radius of the circle of equal 2 cm entered in it. It is required to calculate its area. Decision.Pl =4*2²=16. Answer: 16 cm².
4. To calculate the area of a square if the radius of the circle described around it is set, increase a square of this radius by two. In the form of a formula it looks as follows: Pl = 2P², a gder – the radius of a circumscribed circle. This regularity is brought out of the fact that the radius of a circumscribed circle equals to a half of diagonal of a square. For example, let it is required to calculate the area of a square with a radius of circumscribed circle of 10 cm. Decision.Pl = 2*10²=200 (cm²).
5. For calculation of the area of a square with the known length of its diagonal halve a diagonal square. That is: Pl = d²/2. This dependence follows from Pythagorean theorem. Let, for example, it is necessary to count the area of a square with the diagonal equal of 12 cm. Decision.Pl = 12²/2=144/2=72 (cm²).