Five small squares with a side length of 1 make a big square

The area of the large square is 5, and the side length is root 5
First, put two squares together into a rectangle, cut it along the diagonal, and get two right triangles, whose hypotenuse is root 5. Use the same method to get two right triangles. Surround the four right triangles around the remaining small squares, and get a large square

How to make a big square with two scissors?

According to Pythagorean theorem, take two hypotenuses with right angle sides 1 and 2 (that is, the diagonal connecting the leftmost and bottom square lines is the side length). That's clear enough! Let's divide them for me!

Make a big square by cutting four pieces of cross shaped paper which is composed of five squares

First of all, calculate the side length of the big square. If the side length of five small squares is 1, the total area is 5. So the side length of the big square is root 512345. Cut from the left top of 1 to the right bottom of 3, and this line segment is root 5

There is a big square made up of the same nine squares. How many different painting methods are there if two of them are blackened (if several of them can be made heavy by rotation)

In order to avoid repeated calculation, it can be divided into several categories: 1) one in the middle is blackened, then the other one has only two kinds of painting methods (corner or edge in the middle), the others can be obtained by rotation. 2) there is no blackening in the middle, and two blackened ones are on the corner. 2 (diagonal or adjacent angle) 3) there is no blackening in the middle, and two blackened ones are

Four small squares make up a big square. Use five different colors to paint it. It requires that the small squares with adjacent sides have different colors. How many painting methods are there?

There is a formula for this, but I forgot It should be 260 kinds. The first piece has C51 kinds, and the adjacent piece has only C41 kinds. Then the piece with the opposite angle to the first piece needs to be discussed. When the color is the same as the first piece, the last piece has C41 kinds of painting methods. When the color is different from the first piece, the last piece has only C31 kinds of painting methods. To sum up, there are 5 * 4 * (4 + 3 * 3) kinds, that is 260 kinds
This is based on the fact that Benson's square has a name. If the title has special requirements, it will be different. For example, there is no difference between each block (that is, symmetry should be considered)

As shown in the figure, a large square is made up of a small square and four identical right triangles,
The two right sides of a right triangle are 2 and 5 respectively. What is the area of a large square

The area of a large square is (2 + 5) &# 178; = 48

Four congruent right triangles form a large square, and the empty part in the middle is a small square, thus forming a "Zhao Shuangxian diagram"
If the area of the small square is 1, the area of the large square is 25, and the smaller acute angle of the right triangle is θ, the value of sin θ is obtained

Let the side length of a right triangle be x for the short right side, y for the long right side, and 5 for the hypotenuse,
Then 1 / 2XY = (5 * 5-1) / 4 = 6 (1),
X ^ 2 + y ^ 2 = 25 (Pythagorean theorem) (2),
By combining the solutions (1) (2), we can get: X1 = 3, X2 = 4 (actually y),
So sin θ = x / 5 = 3 / 5

By four sides of ABC right triangle constitute a large square, find the ABC equation
There is an empty small square in the middle

(a+b)^2=ab*4/2+c^2
It's the same area
So a ^ 2 + B ^ 2 = C ^ 2

Divide a large square with a side length of 3cm into nine small squares in two ways

The first method is equal division, that is, the areas of nine small squares are equal. Needless to say, this method. The second method is non equal division, that is, the areas of nine small squares are not equal. First, divide the large square into four small squares, keep three of them, divide the remaining one into nine small squares, and then merge the four adjacent small squares into one

Can you find two different ways to divide a square into nine small squares?

As shown in the figure:

Five small squares with a side length of 1 make a big square