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Area of Rhombus of side 5 and Geometric properties like symmetry,perimeter of rhombus,diagonals of rhombus

Area of a rhombus with side 5 units and base angle 60 degrees = side x side x sine of baseAngle = 5 x 5 x 0.866 = 21.65 square units

Perimeter of a rhombus with side 5 units = 4 * side = 4 * 5 = 20 units

Length of the two Diagonals of a rhombus with side 5 units = 2 * length of side * sin(BaseAngle/2.0) and 2 * length of side *cos(BaseAngle/2.0) = 2 * 5 * sine of 30.0 degrees and 2 * 5 * cosine of 30.0 degrees = 5.0 and 8.66 units

Height of the Rhombus = Area of Rhombus / (length of side) = 4.33 units

The order of symmetry of a rhombus is 2 (number of times the shape co-incides with itself during a 360 degree rotation). The symmetry group is dihedral. And it is isotoxal or edge-transitive in nature, though these are concepts and details which some of you might encounter later.

The number of axes of symmetry of a rhombus is 2: the two diagonals

In general, there are multiple formulas to compute the area of rhombus. Depending on information available you may use either of them.

Area of a rhombus = (square of side) x sine(base Angle) = product of diagonals/2 = base x height


To understand more about the geometric features and properties of a rhombus, formulas related to mensuration etc. you might find it useful to read the properties of a Rhombus tutorial over here. Many of these concepts are a part of the Grade 9 and 10 Mathematics syllabus of the UK GCSE curriculum, Common Core Standards in the US, ICSE/CBSE syllabus in India. Many of these concepts are a part of the Grade 9 and 10 Mathematics syllabus of the UK GCSE curriculum, Common Core Standards in the US, ICSE/CBSE/SSC syllabus in Indian high schools. You may check out our free and printable worksheets for Common Core and GCSE.

An Example of Scale Factor, Similarity, Similar Shapes and Size Transformation

This rhombus (let us call it Rhombus A) has a base angle of 60 degrees and is similar in shape to this rhombus which also has a base angle of 60 degrees, but has an edge of length 2 units (let us call this Rhombus B).

Check the ratios:
(length of side of A) : (length of side of B) = 5 : 2
(area of A) : (area of B) = 25 : 4

This is an illustration of how the ratio of the area of two similar figures is the square of the ratio of the lengths of their corresponding sides. 
This principle holds, not just for the particular shape, but for all similar 2D shapes in general. 

Geometric Properties of a rhombus of side 1 units.



Geometric Properties of a rhombus of side 2 units.



Geometric Properties of a rhombus of side 3 units.



Geometric Properties of a rhombus of side 4 units.



Geometric Properties of a rhombus of side 5 units.



Geometric Properties of a rhombus of side 6 units.



Geometric Properties of a rhombus of side 7 units.



Geometric Properties of a rhombus of side 8 units.



Geometric Properties of a rhombus of side 9 units.



Geometric Properties of a rhombus of side 10 units.




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