Question

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?

Answer 1

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.

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)`