As for the calculation of the area of a square, we usually follow the well-known formula for squared the side length, that is, if the side length of a square is a, then the area of the square can be expressed as a. This easy-to-understand and universally applicable rule makes it easy to solve any given square with equal measurement sides or differences in size or shape.
For the majority of primary school students, by keeping this formula in mind and applying it in practice, such as measuring the size of the square table in our daily life, or conducting a comprehensive in-depth analysis of it and exploring it, this will undoubtedly help to enhance everyone's awareness and understanding of this formula.
In addition, in order to further deepen your understanding, we also recommend the following five methods for calculating the area of a square, including the formula method, the Pythagorean theorem, the cutting method, the translation method, and the rotation method. These clever methods will come into play when we solve the square area. In general, no matter which method is chosen, in the end, it is nothing more than solving for the edge length to finally arrive at the area value of the square.
Therefore, as long as you keep in mind the above formulas for calculating the area of a square and are proficient in using these calculation methods that have contributed a lot, we believe that you will be able to accurately calculate the area of various sizes and shapes of squares in your life.
Cut-and-patch is actually an effective way to turn a seemingly complex problem into a simple problem that is easy to solve, and it can help you quickly calculate the area of the square you need when demand increases dramatically. You can try to divide the square into a rectangle and two right triangles, since the length and width of the rectangle are equal to the length of the sides of the square, we can also determine that the area of the rectangle is the area of the original square. Next, we calculate the area of the two parts of the right triangle, and it is worth noting that the area of the two triangles corresponds to the square of the length of the two sides of the right angle, so the sum of the two is exactly the area value of the original square. Once all the areas have been calculated, simply add the area of the rectangle and the area of the two right triangles, and the final result will be naturally obtained.
The Pythagorean theorem: First, you can coincident one of the vertices of a square with the middle of its diagonal, and then push it diagonally to another vertex until the new vertex exactly overlaps the original vertex. This will give you a new type of square with sides exactly equal to the diagonal of the original square.
Next, quickly calculate the area of the new square, multiply it by two, and the final answer is clear, it is the area of the original square. This is because the area of the new square is exactly equal to the square of the length of the diagonal, which in turn can be measured with the help of the Pythagorean theorem.
All in all, the method of calculating the area of a square using the translation method is not complicated, just follow the steps to coincide one vertex of the square with the midpoint of the diagonal, and then push it along the diagonal to another fixed point, until the new vertex overlaps with the original vertex to form a new square. Then, starting from the area of the new square and multiplying it by 2, the area of the original square can be obtained smoothly. First, we need to rotate the square 45 degrees along an axis so that it becomes a parallelogram. We can then measure and calculate the lengths of the two diagonals of the parallelogram and add them together to get a new edge length. Finally, we follow the formula, where the square of the side length represents the area, and multiply the new side length by 2 to easily get the area value of the square. This approach takes full advantage of the specific properties of the square diagonal, optimizes and simplifies the computational process, which can be more complex, and thus improves the computational efficiency.