How do you calculate the area of a rectangle with a diagonal?

PassedDiagonalCalculate the area of the square: s=1 2a 2 (where a is the length of the diagonal).

Example: A problem to find the area of a shadow rectangle, a triangle, where the shaded part is a rectangle, in the figure, the specific length of the length and width of the rectangle is not given, to calculate the area of the rectangle, you must know the values of length and width, and then multiply the length by the width to calculate the area.

After drawing the auxiliary line, the students carefully observed that the new shape is a large rectangle, how to only look at the diagonal line in the middle, we will find that this large rectangle is evenly divided into two right triangles.

The area of the black shaded part is equal to the area of the red shaded part. The red part, according to the data already given in the question, is 20 centimeters long, 5 centimeters wide, 20 times 5, and the area is 100 square centimeters.

Math skills for 6th grade.

In the sixth grade, the triangle resemblance has not yet been learned.

Therefore, when understanding the calculation method of this question, parents also have to explain the specific truth to their children.

Otherwise, at the level of mathematics of elementary school students, there will be some obstacles in understanding. However, as long as you can find the area of the triangle, you can still understand similar triangles. Target.

It should be:"Calculate the area of the square by diagonal lines"bar. If yes, then s=1 2a2 (where a is the length of the diagonal).

If you don't know the angle of the diagonal, you can't calculate it.

If it is known that the diagonal of the rectangle cannot find the area, it is also related to the angle of the diagonal.

The area corresponding to different angles is also different.

Let the angle between the diagonals be x, and the length of the diagonal is m

Then the area formula is s=(m2 2)*sinx

RectangularDiagonalIt is calculated as follows: the diagonal line is equal to the sum of the squares of the long square and the widening of the square.

For example, if the length is 3 and the width is 4, then the square of diagonal = 3 plus the sum of the squares of 4 (i.e. 25) is squared and finally 5.

The nature of the diagonal line of the rectangle:

1. It has a parallelogram.

of all properties, the opposite sides are parallel and equal, the diagonal is equal, the adjacent angles are complementary, the diagonals are bisected from each other, and the four corners are all right angles; It has equal diagonal lines and is unstable (easily deformed).

2. A rectangle is also called a rectangle. A rectangle is a quadrilateral with at least three inner angles that are all right angles. A rectangle is a special type of parallelogram, and a square is a special rectangle. Since the rectangle is a special parallelogram, it contains the properties of a parallelogram.

Formula: l= (a +b). where A and B represent the length and width of the rectangle, respectively, and L represents the diagonal length of the rectangle.

The square of the diagonal length of the rectangle is the sum of the squares of the two sides. The two diagonals of the rectangle are equal, and the two diagonals are bisected from each other.

Derivation processThe square of the length + the square of the width = the square of the diagonal.

Solution: Make the length of the rectangle a, the width of the rectangle b, and the diagonal of c.

Since the four corners of the rectangle are all right angles, the length, width, and diagonal lines of the rectangle form a right triangle.

Then according to the triangular properties, a 2 + b 2 = c 2. C= (A2+B2).

For example, the rectangle of length 4 and width 3 is 4*4+3*3=25, and the square root of 25 is 5.

Question: How many degrees do I ask?

cos sin tan

Can I ask a question?

tan a ＝3/4

a 37° Hello, can you list the details?

tan a ＝b/a＝3/4

A 37° question, but I don't have the letter A on my phone.

That one is Alpha.

The angle can't be calculated with a calculator.

Question: What is the use of that?

It can be calculated using the Pythagorean theorem that the length + width of the rectangle = the square of the diagonal.

The diagonal length of the rectangle is calculated using the Pythagorean theorem:

7 meters long, 3 meters wide, diagonal length of the rectangle = (length + width and width) = (7 + 3) = 58 meters).

Three meters wide, four and a half meters long, the diagonal length of the rectangle = (length length + width width) = (meters).

The sum of the lengths of the two right-angled sides of any diagonal triangle formed by the diagonal line (the sum of the length, width, square of the rectangle or square, and the square root of the re-opening square is the length of the diagonal. For example, the diagonal of a rectangle with a length of 4 and a width of 3 is 4*4+3*3=25, and 25 is 5

poervfu 2014-10-29

The diagonal of the rectangle is equal to: the square of the long and the widened square, and the re-root.

The diagonal of the rectangle is calculated as follows:1. The angle of the rectangle is a right angle, and the length, width, and diagonal lines form a right triangle.

2. The formula for the side length of a right-angled triangle is: a?+b?=c?。

3. So the diagonal of the rectangle: c= (a?+b?）。

A diagonal, a geometric term, is defined as a line segment that connects any two non-adjacent vertices of a polygon, or any two vertices of a polyhedron that are not on the same face.

Because the diagonal of the rectangle divides the rectangle into two right triangles, the length of the diagonal can be found using the Pythagorean theorem. For example, a rectangle is a in length, a b in width, and a c:

The diagonal c of the rectangle is actually the hypotenuse of the right triangle ABC, so the length of the diagonal is:

c=√（a²+b²）。

Knowing the diagonal of a square, the method of finding the side length is as follows:

Analysis and Answer: As shown in the figure above.

Two diagonal lines divide the square into exactly the same 4 small isosceles right triangles.

The right-angled side of each small isosceles straight-sensitive muffled triangle = half of the diagonal of the square;

Because the length of the diagonal is known, the length of the right-angled side of the small triangle can be found, and then the area of the small triangle can be found.

The area of the small triangle 4 is the area of the square, and the side length can be found according to the area formula of the square.

Here you can calculate the side length of the square by making the diagonal length of the square 8 cm.

Solution: 8 2 = 4 (cm).

The area of a small triangle is 4 4 2 = 8 (square centimeters) and the area of a square = 8 4 = 32 (square centimeters).

If the side length of the square is a, then a = 32, a = root number 32 = 4 times the root number 2 A: The side length of a square with a diagonal of 8 cm is 4 times the root number 2 cm.

If you haven't learned the root number, you can only find the range of the side length:

5 32 6, so the side length a is between 5 and 6.

Summary. For example, if the area of a square is equal to four, the length of that side is equal to two, and the diagonal is equal to the root number eight.

Know how to find the length of the diagonal in the square area.

Hello, I have seen your question and am sorting out the answer, please wait a while Hello, I know the area of the square. You open the area with a root number, which is the side length. Then the square of the side twice the length of the root number is the length of the diagonal.

For example, if the area of a square is equal to four, the length of that side is equal to two, and the diagonal is equal to the root number eight.

No functions, just elementary school methods.

This is useless, if it's an elementary school, the area of the square should be a special value, right?

Said in sections. I should have learned the square in elementary school, so this has to be the side length, you open a square in the root number, that is, the diagonal is long.

It's the Pythagorean theorem.

It's very simple.