Two rhombuses have sides with lengths of #8 #. 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?

Question

Two rhombuses have sides with lengths of #8 #.  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?

Ella Armstrong · Accepted Answer

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.

Evelyn Arboleda · Answer

undefined To find the area of a rhombus, you can use the formula: Area = (diagonal1 * diagonal2) / 2.

Given that both rhombuses have sides of length 8, we can calculate their diagonals. The diagonals of a rhombus are perpendicular bisectors of each other.

For the rhombus with an angle of π/12, the diagonals will have lengths of 8 and 8 * tan(π/12).

For the rhombus with an angle of (5π)/8, the diagonals will have lengths of 8 and 8 * tan((5π)/8).

Once you find the lengths of the diagonals for both rhombuses, plug them into the area formula and find the difference in their areas.

Avery Allen · Answer

undefined The difference between the areas of the rhombuses is $ 32 - 32\sqrt{2} $ square units.