Two rhombuses have sides with lengths of #8 #. If one rhombus has a corner with an angle of #(5pi)/12 # and the other has a corner with an angle of #(7pi)/12 #, 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 #(5pi)/12  # and the other has a corner with an angle of #(7pi)/12  #, what is the difference between the areas of the rhombuses?

Aaliyah Anderson · Accepted Answer

Since both the parallelograms are identical, difference in areas is 0

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.

Ella Armstrong · Answer

undefined To find the area of a rhombus, you can use the formula: Area = (diagonal1 * diagonal2) / 2. Since the diagonals of a rhombus bisect each other at right angles, the formula simplifies to: Area = (d1 * d2) / 2, where d1 and d2 are the lengths of the diagonals.

For the given rhombuses with side lengths of 8, the diagonals can be calculated using trigonometry. The diagonals are twice the length of the side multiplied by the cosine of the angle at one of the corners.

For the first rhombus with an angle of (5pi)/12:
diagonal1 = 2 * 8 * cos((5pi)/12)

For the second rhombus with an angle of (7pi)/12:
diagonal2 = 2 * 8 * cos((7pi)/12)

Calculate the values of diagonal1 and diagonal2 using a calculator.

Then, use the formula for the area of a rhombus to find the areas of both rhombuses.

Finally, subtract the smaller area from the larger area to find the difference between the areas of the two rhombuses.