Two rhombuses have sides with lengths of #4 #. If one rhombus has a corner with an angle of #(5pi)/12 # and the other has a corner with an angle of #(3pi)/8 #, what is the difference between the areas of the rhombuses?

1 Answer
sankarankalyanam
Dec 9, 2017

Difference in areas between two rhombuses is 19.9912

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 = 4 * sin ((3pi)/8) = 3.6955#
Area = a * h = 4 * 3.6955 = 14.782#

Rhombus 2
#h = a sin theta = 4 * sin ((5pi)/12) = 8.6933#
Area = a * h = 4 * 8.6933 = 34.7732

Hence the difference in areas is #34.7732 - 14.782 = 19.9912#

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