Two rhombuses have sides with lengths of #15 #. If one rhombus has a corner with an angle of #(3pi)/8 # and the other has a corner with an angle of #(5pi)/6 #, what is the difference between the areas of the rhombuses?

Question

Two rhombuses have sides with lengths of #15 #.  If one rhombus has a corner with an angle of #(3pi)/8  # and the other has a corner with an angle of #(5pi)/6  #, what is the difference between the areas of the rhombuses?

Sadie Adams · Accepted Answer

Difference in areas between two rhombuses is 12.2238

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.

Noah Atkinson · Answer

undefined To find the area of a rhombus, you can use the formula: Area = (diagonal 1 * diagonal 2) / 2.
Given the side length of the rhombus is 15, the diagonals can be calculated using trigonometry.
For the first rhombus with an angle of (3π)/8, we can use the sine function to find the diagonal: diagonal = 2 * side * sin(angle).
For the second rhombus with an angle of (5π)/6, we can also use the sine function to find the diagonal.
After calculating the diagonals for both rhombuses, plug the values into the formula to find their respective areas.
Once you have the areas of both rhombuses, subtract the smaller area from the larger area to find the difference.