Question

Two rhombuses have sides with lengths of `12`. If one rhombus has a corner with an angle of `pi/3` and the other has a corner with an angle of `(5pi)/8`, what is the difference between the areas of the rhombuses?

Answer 1

≈ 8.33 square units

Explanation:

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

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

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^2 sintheta = a^2 sintheta`

hence area of 1st rhombus `= 12^2sin(pi/3) ≈ 124.71`

and area of 2nd rhombus `= 12^2sin((5pi)/8) ≈ 133.04`

difference in area = 133.04 - 124.71 = 8.33 square units