Calculate the diagonal of the area in the square

What you need:

• Paper, pencil
• calculator
• Pythagorean theorem
• some time and patience

Calculate surface diagonals - this is how it works in a square

• In the case of a square, all four sides a are the same length, for example a = 3 cm. In addition, all four sides of a square are perpendicular to each other, they form a right one angle.
• Each square has two surface diagonals, which, however, are also of the same length because of the sides of the same length. With a diagonal you connect the opposite corners of the square. You can see immediately that the surface diagonals are longer than the sides of the square. Because of the diagonals, the square "splits" into two Trianglesthat are isosceles and include 90 ° as a top angle. In these triangles, the Pythagorean theorem applies (which only applies to right-angled triangles!).
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• If you add the two cathetus squares, you get the hypotenuse square, better known as a² + b² = c². You apply the theorem for calculating the surface diagonals. In this case, take the diagonal d as the hypotenuse (longest side of the triangle and the right angle opposite).
• The two legs are the same and correspond to the side length a of the square. So you calculate: a² + a² = d² or 2 a² = d². You can solve this quadratic equation for the surface diagonal d: You simply pull the root (calculator).

Area diagonal - example and general formula

• The above-mentioned example square with a = 3 cm is used again.


Calculate the diagonal of the surface for the cube

The game cube is the simplest geometric body. Surface diagonal, ...

• You calculate: a² = 9 and 2 a² = 18. So you get d² = 18 and d = 4.24 cm.
• In general you calculate (without inserting the numbers): d = root (2 a²) = a _* Root (2) = a * 1.41 (if you round to two places behind the decimal point).

So you can either - as in the example - the Counting directly or use the formula above.