Question

Two rhombuses have sides with lengths of `12`. 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?

Answer 1

no difference.Area's are equal.

Explanation:

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

The area of 1 triangle `= 1/2 a.a sintheta = 1/2 a^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 `=12^2sin((5pi)/12) ≈ 139.093`

and area of 2nd rhombus`= 12^2sin((7pi)/12) ≈ 139.093`

Area's of both are equal hence no difference.