Two rhombuses have sides with lengths of #15 #. If one rhombus has a corner with an angle of #pi/12 # and the other has a corner with an angle of #pi/4 #, what is the difference between the areas of the rhombuses?

1 Answer
Dec 9, 2017

Difference in areas between two rhombuses is 100.8645

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 = 15 * sin ((pi)/4) = 10.6066#
Area = a * h = 15 * 10.6066 = 159.099#

Rhombus 2
#h = a sin theta = 15 * sin ((pi)/12) = 3.8823#
Area = a * h = 15 * 3.8823 = 58.2345#

Hence the difference in areas is #159.099 - 58.2345 = 100.8645#