SOLUTION: The four sides and one diagonal of a rhombus each have sides 3√6 cm long. Find the area of the rhombus, in cm^2.

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Question 1209054: The four sides and one diagonal of a rhombus each have sides 3√6 cm long. Find the area of the rhombus, in cm^2.
Found 3 solutions by ikleyn, math_tutor2020, MathTherapy:
Answer by ikleyn(52787)   (Show Source): You can put this solution on YOUR website!
.
The four sides and one diagonal of a rhombus each have sides 3√6 cm long.
Find the area of the rhombus, in cm^2.
~~~~~~~~~~~~~~~~~~ 

Obviously, the diagonal of  cm  divides this rhombus in two 

equilateral congruent triangles with the sides length  a =  cm.



The area of each such a triangle is  

     =  =  =  = .


Hence, the area of the rhombus is the doubled area of any of the two triangles   cm^2.    ANSWER

Solved.



Answer by math_tutor2020(3817)   (Show Source): You can put this solution on YOUR website!

Here is a diagram to supplement the answer that tutor ikleyn has given
Answer by MathTherapy(10552)   (Show Source): You can put this solution on YOUR website!
The four sides and one diagonal of a rhombus each have sides 3√6 cm long. Find the area of the rhombus, in cm^2.


Since one of its diagonals is equal to its sides, then 2 EQUILATERAL triangles will emerge, to form the rhombus

Each angle of each equilateral triangle =  = 60o
Area of any NON-RIGHT triangle =  the PRODUCT of 2 of its CONSECUTIVE sides, TIMES the sine of the INCLUDED angle 
So, AREA of one of this rhombus' 2 equilateral triangles =  =  
                                                                                   --- Substituting  for sin 60o
As there are 2 of these equilateral triangles, AREA of both equilateral triangles/RHOMBUS =  =  =
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