Two rhombuses have sides with lengths of #9 #. If one rhombus has a corner with an angle of #pi/12 # and the other has a corner with an angle of #pi/3 #, what is the difference between the areas of the rhombuses?

1 Answer
sankarankalyanam
Dec 9, 2017

Difference in areas of Rhombus s = 34.6743

Explanation:

Area of rhombus #= (1/2) * d_1 * d_2 or a * h#
Where #d_1 , d_2 # are the diagonals, a is the side and h is the altitude.

In this case we will use the formula Area = a * h.
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Rhombus 1
#h = a sin theta = 9 * sin (pi/12) = 11.6469#
Area = a * h = 9 * 11.6469 = 104.8221#

Rhombus 2
#h = a sin theta = 9 * sin (pi)/3 = 7.7942#
Area = a * h = 9 * 7.7942 = 70.1478#

Hence the difference in areas is #104.8221-70.1478 = 34.6743#

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