The geometric diagram figure is a variation of a parallelogram having equal side. Its height is part of a straight line, passing through the top of the shape and forming an angle of 90 ° when crossed with the opposite side. A special case of rhombus is a square. Knowledge of the properties of rhombus, as well as the right graphical interpretation of the conditions of the task allow you to correctly determine the height of the figure using one of the permissible methods.
Finding the height of diamond on the basis of the data on the area of \u200b\u200bthe figure
Before you is a rhombus. As is known, to find its area, it is necessary to multiply the part of the side to the numerical value of the height, i.e. S \u003d k * h where
- k is a value that determines the length of the side of the figure,
- H is a numeric value corresponding to the length of the rhombus height.
This ratio allows you to determine the height of the figure as: H \u003d S / K(S - Roma Square, known by the condition of the task or the previously calculated, for example, as half of the product of the diagonals of the figure).
Finding the height of rhombus through the inscribed circle
Regardless of the length of the sides and the magnitude of the corners of the rhombus, it can be written around the circle. The center of this geometric shape will coincide with the point of intersection of the diagonals of the equilateral parallelogram. Information about the magnitude of the radius of such a circle will help determine the height of the rhombus, because R \u003d H / 2, where:
- r is a radius inscribed in a diamond circle,
- H is the search for the height of the figure.
From this relation, it follows that the height of the equilibrium parallelogram corresponds to the doubled radius inscribed in this parallelogram of the circle - H \u003d 2r..
Finding the height of rhombus through the magnitudes of the corners of the figure
Before you, the MNKP rhombus, the side of which Mn \u003d nk \u003d kp \u003d pm \u003d m. Through the vertex m, 2 straight lines were held, each of which forms with an opposed side (NK and KP) perpendicular - height. Denote them as MH and MH1, respectively. Consider the triangle MNH. It is rectangular, which means that knowing ∠n and the definition of trigonometric functions, you can determine its side-height of the rhombus: sinn \u003d mh / mn ⇒ MH \u003d Mn * sinn, where:
- sINN - sinus angle at the top of the equilateral parallelogram (rhombus),
- Mn (m) - the size of the specified rhombus.
Because Roma angles lying opposite each other are equal to each other, the value of the second perpendicular, lowered from the vertex M is also defined as the MN product on SINN.
H \u003d M * sinn- The height of such a figure as a rhombus can be determined by multiplying the numerical value of the length of its side to the corner sinus during its vertex.
Having determined the length of the same height of the rhombus, you get information about the magnitude of the remaining three perpendicular figures. This conclusion follows that the rhombus is equal to each other.
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