Question

Two rhombuses have sides with lengths of `5`. If one rhombus has a corner with an angle of `pi/2` and the other has a corner with an angle of `(3pi)/8`, what is the difference between the areas of the rhombuses?

Answer 1

Difference in areas of the rhombuses is 1.903

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.

Rhombus 1
#h = a sin theta = 5 * sin ((pi)/2) = 5 Area = a * h = 5 * 5 = 25#

Rhombus 2
`h = a sin theta = 5 * sin ((3pi)/8) = 4.6194`
Area = a * h = 5 * 4.6194 = 23.097#

Hence the difference in areas is `25 - 23.097 = 1.903`