SOLUTION: The four sides and one diagonal of a rhombus each have sides 3 sqrt1/3 cm long. Find the area of the rhombus, in cm2.

Algebra ->  Surface-area -> SOLUTION: The four sides and one diagonal of a rhombus each have sides 3 sqrt1/3 cm long. Find the area of the rhombus, in cm2.      Log On


   

Question 1149184: The four sides and one diagonal of a rhombus each have sides 3 sqrt1/3 cm long. Find the area of the rhombus, in cm2.
Answer by ikleyn(52781) About Me  (Show Source):
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The rhombus is comprised of two EQUILATERAL triangles with the side length of  a = 3%2Fsqrt%283%29 = sqrt%283%29 centimeters.


The area of each of the two equilateral triangles is  a%5E2%2A%28sqrt%283%29%2F4%29 = %28sqrt%283%29%29%5E2%2A%28sqrt%283%29%2F4%29 = 3%2A%28sqrt%283%29%2F4%29%29 = %283%2Asqrt%283%29%29%2F4 cm^2.


Hence, the area of the rhombus is twice this value, i.e.  %283%2Asqrt%283%29%29%2F2 cm^2.       ANSWER

Solved.