Two rhombuses have sides with lengths of #7 #. If one rhombus has a corner with an angle of #pi/4 # 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

Both the areas are the same and hence no difference in areas.

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 = 7 * sin ((pi)/4) = 4.9497#
Area = a * h = 7 * 4.9497 = 34.6479#

Rhombus 2
This also has the same side length and the angle and hence the area also the same.

Hence the difference in areas is #color(red)(0)#