Two rhombuses have sides with lengths of #2 #. If one rhombus has a corner with an angle of #pi/8 # and the other has a corner with an angle of #(5pi)/12 #, what is the difference between the areas of the rhombuses?

1 Answer
sankarankalyanam
Dec 9, 2017

Difference in areas between two rhombuses 2.333

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 = 2 * sin ((pi)/8) = 0.7654#
Area = a * h = 2 * 0.7654 = 1.5308#

Rhombus 2
#h = a sin theta = 2 * sin ((5pi)/12) = 1.9319#
Area = a * h = 2 * 1.9319 = 3.8638#

Hence the difference in areas is #3.8638 - 1.5308 = 2.333#

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