Two rhombuses have sides with lengths of #6 #. If one rhombus has a corner with an angle of #pi/12 # and the other has a corner with an angle of #(7pi)/8 #, what is the difference between the areas of the rhombuses?

1 Answer
Dec 10, 2017

Difference in areas between the two rhombuses is 4.4592

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 = 6 * sin ((pi)/12) = 1.5529#
Area = a * h = 6 * 1.5529 = 9.3174#

Rhombus 2
#h = a sin theta = 6 * sin ((7pi)/8) = 2.2961#
Area = a * h = 6* 2.2961 = 13.7766#

Hence the difference in areas is #13.7766 - 9.3174 = 4.4592#