Know the side length of the square and find the diagonal of the square

Squares are special rectangular shapes.

Since the diagonal formula of the rectangle is the square of the long and widened square, then the square is opened.

And what about the square ones? Think about it!

What the? Can't think of it?

Then I'll tell you:

Let's set the side length to A.

a^2+a^2)=√(a*a+a*a)=√[(2a)*a] =√(2a²)

Cut the square along one of the diagonals and put it together into a new triangle, because it is diagonal, so the two corners are 45 degrees, and the new triangle is a right triangle. The square and triangle are equal in area, i.e. the diagonal length multiplied divided by 2 = side length multiplied by side length. The operator symbol cannot be typed.

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Square ABCD, diagonal AC.

Extend AB to E so that AB=BE, linking CE.

The angle ace = 90 degrees can be obtained. So the triangle ace is an isosceles right triangle.

The length of ac is obtained by multiplying ac by ce=bc multiplied by ae, and ac=ce.

I don't know if it's okay.

Well, it's simple. No need for the Pythagorean, teach you, multiply the two diagonals and divide by 2!

Use the area, with two diagonals, to calculate the area of two isosceles right triangles.

Personally, I can only think of the Pythagorean theorem, which is basically memorized, the diagonal length is twice the root number of the side length.

It can be deduced by the method of area, side length x side length = diagonal x diagonal, or directly with the conclusion: diagonal = side length x root number 2.

The two opposite sides of the square are parallel to each other, and all four sides are equal; All four corners are 90°; The diagonals are perpendicular, bisected, and equal to each other, with each diagonal bisecting a set of diagonals.

A group of parallelograms with equal adjacent sides and one corner at right angles is called a square. There is a group of rectangles with equal adjacent sides called squares, and there is a diamond with an angle of 90° called a square. The square is a special form of a rectangle and a special form of a diamond.

Determination theorem1. A diamond with equal diagonals is a square.

2. A diamond with a right angle is a square.

3. Rectangles with diagonal lines perpendicular to each other are squares.

4. A group of rectangles with equal adjacent sides is a square.

5. A group of parallelograms with equal adjacent sides and one angle is a right angle.

6. A parallelogram with diagonal lines perpendicular to each other and equal to each other is a square.

7. Quadrilaterals with equal diagonals and perpendicular bisects are squares.

Let the side length of the square be a, and you can use the triangle area method. Divide into two right triangles along the diagonal. The area of a triangle is 1 2a squared.

It is also half of a diagonal line multiplied by 1 2 of the length of another diagonal. Even 1 to 4 diagonals squared. At this point, you can find the length of the diagonal.

Finding the diagonal of the known side length of a square can bypass the Pythagorean theorem, but you can't avoid writing the root number to find the square root, because the answer to this question is.

The diagonal length of the square = 2 times the length of the sides.

Take a look at the diagram.

There is no specific topic, take a picture.

Squares can be used diagonally perpendicular to each other; The diagonals are equal and bisected from each other; Each diagonal divides a set of diagonal basic properties to find the side length of a square.

Example: The difference between a cube and a square.

1. Different faces: The cube has 6 faces, which is a three-dimensional figure, and the square has only 1 face, which is a plane figure.

2. The surface area of the cube and the square are not the same, the area of the cube is generally said to be the surface area, which is the sum of the area of 6 faces, while the area of the square is only 1 face, so the area of the cube is 6 times that of the square with the same side length.

3. The statement that the square has no volume, because it is a flat figure, only the area has no volume, and the cube has volume as a three-dimensional figure.

You really don't need the Pythagorean theorem, just know that the triangle is looking for the area.

Diagonal x Diagonal x1 2 = square area.

Square area = side length x side length.

If the problem has been solved, click on the lower right to adopt.

a is a known number, then the side length is x

Ask the square diagonal meter and find the side length.

23 root number 2 20

Ask a question, I want results.

That's all there is to the side length.

Ask how many meters the side is long.

23 root No. 2 20 m.

Ask me about the exact length I want, not the work style.

That's the length.

It can't be simplified anymore.

The diagonal of the square.

Equal to 2 times the length of the side, because according to the Pythagorean theorem.

Available: Diagonal = side length + side length, the Pythagorean theorem, is a basic geometric theorem that refers to a right triangle.

The sum of the squares of the two right-angled edges is equal to the hypotenuse.

of the squared. In ancient China, the right triangle was called the Pythagorean shape, and the smaller of the right-angled sides was the hook, the other long right-angled side was the strand, and the hypotenuse was the chord, so this theorem was called the Pythagorean theorem, and some people called the Shanggao theorem.

The Pythagorean theorem now has about 500 ways to prove it, making it one of the most provable theorems in mathematics. The Pythagorean theorem is one of the important mathematical theorems discovered and proven by mankind in the early days, one of the most important tools for solving geometric problems with algebraic ideas, and it is also the combination of numbers and shapes.

one of the bonds.

The two sides of the diagonal line and the square form an isosceles right triangle, and the square of the diagonal can be found using the Pythagorean theorem, which is the sum of the squares of the two right-angled sides. Then find the arithmetic square of this Ho, and the root can find the length of the diagonal.

Diagonal = side length + side length

The diagonal of the square = 2 times the length of the side

A diagonal line divides the square into two congruent isosceles triangles.

So the diagonal is equal to 2 times the length of the side.

Let the diagonal length be a and the side length x, then.

a 2 = 2 x 2, i.e. x = ((a 2) 2) (1 2), text: half of the square of the diagonal length, then squared.

Summary. Hello, dear, it is a pleasure to help you learn to find the diagonal of the known side length of the square, which can be calculated according to the Pythagorean theorem.

How do you find the diagonal of the known side length of a square?

Hello, dear, it is a pleasure to help you learn to find the diagonal of the known side length of the square, which can be calculated according to the Pythagorean theorem.

The square of the hypotenuse of a right triangle is equal to the sum of the squares of the two right angles.

The hypotenuse here refers to the diagonal line of the square, and the two right-angled sides refer to the length of the sides of the square.

I am in the 6th grade of elementary school.

If it is an elementary school, it can be calculated according to the area formula.

The area of the triangle is equal to the base multiplied by the height divided by two.

That is, the area of the square.

It can be calculated by side length, or by diagonal lines.

How to calculate columnarily.

It is recommended that you provide your actual problem, because you are in elementary school, and it is not convenient to teach you algebra.

The sides of the square are known to be 4 cm long.

If the side length of the square is four centimeters, then the area of the square is 16 square centimeters.

Let the diagonal be 2a, then 2a a 16

In general, this problem is calculated according to a circle, and then the largest square of a circle, to get the square of the radius.

The area of the circle is then calculated from the square of this radius.

It's not substantively how much the diagonal is equal to, because I haven't learned it in elementary school.

How to do this question.

Doesn't this have the same truth as my analysis?

It's a combination of a square and a circle!

Just follow my tips above, get the square of the radius of the circle, and you can smoothly calculate the area of the circle, know the area of the circle, and then subtract the area of the square, which is the area of the shaded part.

Please give me a complete list of calculations and prompt you to give the actual problem at the beginning.

From the very beginning, I knew that you were related to such a stereotype.

So there is no need to calculate how long the diagonal is, the main thing is to know the square of the radius of the circle.

Summary. I once encountered this problem in a math class at school, where our teacher showed us how to find the diagonal of a square. The Pythagorean theorem can be used to solve the diagonal line of a square, i.e., the length of the diagonal is equal to the square root of the length of the sides of the square, i.e., d = a, where d is the length of the diagonal and a is the length of the sides of the square.

Alternatively, it can be solved using a trigonometric function, i.e., d=2a*sin(45°), where d is the length of the diagonal and a is the length of the sides of the square. Extension: The diagonal length of a square can also be solved with other trigonometric functions, such as d=2a*sin(30°), d=2a*sin(60°), etc.

I once encountered this problem in my math class at school, when my teacher explained how to find the diagonal of a square. The Pythagorean theorem can be used to solve the diagonal line of a square, that is, the length of the diagonal is equal to the square root of the side length of the square, i.e., the beam shed d = a, where d is the length of the diagonal and a is the side length of the square. Alternatively, it can be solved using a trigonometric function, i.e., d=2a*sin(45°), where d is the length of the diagonal and a is the length of the sides of the square.

Extension: The diagonal length of a square can also be solved with other trigonometric functions, such as d=2a*sin(30°), d=2a*sin(60°), etc.

Excuse me, but please go into more detail?

1.The diagonal length of a square is equal to the square root of its side length, i.e., a, where a is the side length of the square. 2.

The diagonal length of the square is 2 times the length of its sides, i.e. the diagonal length of the square can also be obtained using the Pythagorean theorem, i.e., a2+a2=c2, where c is the diagonal length of the square. The diagonal length of a square can be found in a variety of ways, such as finding the square root, finding 2 times the side length, and using the Pythagorean theorem to find it.