Question

Two rhombuses have sides with lengths of `9`. If one rhombus has a corner with an angle of `pi/6` and the other has a corner with an angle of `(pi)/4`, what is the difference between the areas of the rhombuses?

Answer 1

≈ 16.79 square units

Explanation:

A rhombus has 4 equal sides and is constructed from 2 congruent isosceles triangles.

The area of 1 triangle `= 1/2a.asintheta = 1/2a^2sintheta`

where a is the length of side and `theta" the angle between them "`

Now the area of 2 congruent triangles ( area of rhombus) is

area `=2xx1/2a^2sintheta = a^2sintheta`

Hence area of 1st rhombus `= 9^2sin(pi/6) = 40.5`

and area of 2nd rhombus `= 9^2sin(pi/4) ≈ 57.29`

so difference in area = 57.29 - 40.5 = 16.79 square units