How to find the diamond area?

How to find the diamond area?

  • From school I remember that you can find out the area of ​​this figure as follows:

    • multiply the diagonals and divide by two (2)
    • multiply the height of the figure by the length of the side

    For example, if the diagonal diamonds have a length of 5 and 6 cm, then the area of ​​the diamond is 15 cm. That is, multiplies 5 by 6 and divide by 2.

  • The area of ​​a rhombus S can be found in several ways: 1) S = a * a * sinA = a ^ 2 * sinA, where a is the side of the rhombus, A is the angle between the sides.2) S = a * h, where a is the side of the rhombus, h-height, lowered to the side of the vertex.3) S = d1 * d2, where d1, d2-diagonal of the rhombus. You do not need to divide 2, just multiply the diagonals!

  • Just like a parallelogram, a rhombus is a special case of a parallelogram.

  • This is easy to do.

    It is necessary to multiply one diagonal to another. The resulting work is further divided in half. This will be the required area of ​​such a figure as a rhombus.

    The difficulty is that in problems, as a rule, you first need to find out what the diagonal of the rhombus is equal to.

  • It is necessary to multiply its diagonals and divide the product in half. In order not to cram and not to confuse, you can somehow explain this process for yourself. Personally, I resorted to this trick at school. Diagonals divide the rhombus into 4 right triangles. Adding four more of the same, we get a rectangle in which this diamond is inscribed. Its area is equal to the product of the sides, which are equal to the diagonals of the rhombus. At the same time, the area of ​​the rectangle itself is 2 times the area of ​​the rhombus. Therefore, the area of ​​the diamond is equal to half the area of ​​the rectangle in which it is inscribed. This is a long time to explain in words, but the picture speaks for itself.

    How to find the diamond area?

  • A rhombus is a parallelogram in which all sides are equal. A square is also a rhombus, it is a special case. to calculate the area of ​​the rhombus, there is a formula:

    S = 1 / 2 d1 * d2, where d1, d2 are the diagonals of the rhombus. That is, the area of ​​the rhombus is equal to half the product of its diagonals.

    Since a rhombus is a parallelogram, the area is also equal to the product of its side to a height.

  • You can calculate the area of ​​a rhombus in various ways. The simplest formula, in my opinion, is the product of the length of the perpendicular, drawn from a corner to the opposite side, and the length of this side.

    For clarity, I place a schematic view of the search for a rhombus area.

    How to find the diamond area?

    According to another method, knowing the distance of two diagonals of a figure, it is easy to make the desired calculation.

    How to find the diamond area?

  • The area of ​​a rhombus is determined by the intersection of two straight lines in the middle of a given geometric figure; this is done quite simply by drawing two lines directly revealing the area of ​​the rhombus, which directly depends on the sides of the same rhombus.

  • In order to find the area of ​​a rhombus, you need to know that the area of ​​a rhombus is equal to half the works of its diagonals. This is the children learn in the eighth grade. Also, you need to know that the rhombus is a parallelogram, its area is also equal to the product of its side and its height.

  • There are three options for finding the rhombus area, depending on the source data:

    1) given the base (a) and height (h). S = a * h.

    2) are given side (a) and angle between them (y). S = a * a * sin (y).

    3) are given the sizes of the diagonals (d1 and d2). S = d1 * d2 / 2.

  • The area of ​​a diamond can be calculated by several formulas, it is important to know at least some values ​​that characterize it.

    If its diagonals are known, then the area is the product of the diagonals, divided into two.

    If you know his side and height, then they need to be multiplied to find out the area.

  • Translated from the Latin word rhombus means tambourine. This explains a lot for card game lovers. Just in ancient times, tambourines were made not round, but in the form of parallelograms. Since the rhombus is a parallelogram, then The diamond square can be found in several ways..

    First, the rhombus area is half the product of its diagonals. Many people remember this from school.

    Secondly, the area of ​​a rhombus is equal to the product of its side to a height.

    And thirdly, the area of ​​a rhombus is equal to the product of the square of its side and the sine of the adjacent angle.

    How to find the diamond area?

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