Two rhombuses have sides with lengths of #1 #. If one rhombus has a corner with an angle of #pi/12 # and the other has a corner with an angle of #(5pi)/8 #, what is the difference between the areas of the rhombuses?

1 Answer
sankarankalyanam
Dec 9, 2017

Difference in areas between the two rhombuses is 0.6651

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 = 1 * sin ((5pi)/8) = 0.9239#
Area = a * h = 1 * 0.9239 = 0.9239#

Rhombus 2
#h = a sin theta = 1 * sin ((pi)/12) = 0.2588#
Area = a * h = 1 * 0.2588 = 0.2588#

Hence the difference in areas is #0.9239 - 0.2588 = 0.6651#

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