Question

Two rhombuses have sides with lengths of `7`. 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

The difference between the areas of the rhombuses is `10.15(2dp) sq.unit`

Explanation:

We know the area of rhombus is `A_r= s^2*sin theta` where `s` is the length of sides and `theta` is the angle of a corner. So the Area of first rhombus is`A_(r1)=7^2*sin(pi/6)=49sin30=49*1/2=24.5 sq.unit`
Area of second rhombus is`A_(r2)=7^2*sin(pi/4)=49sin45=49*1/sqrt2=34.65 sq.unit :.`The difference between the areas of the rhombuses is `=A_(r2)-A_(r1)=34.65-24.5=10.15(2dp) sq.unit`[Ans]