Question

Two rhombuses have sides with lengths of `9`. If one rhombus has a corner with an angle of `pi/12` and the other has a corner with an angle of `(7pi)/8`, what is the difference between the areas of the rhombuses?

Answer 1

Difference between their areas `10.04sq.unit`

Explanation:

The sides and a corner with angle of 1st rhombus are `9,/_theta_1=pi/12=15^0`;
The sides and a corner with angle of 2nd rhombus are `9,/_theta_2=(7pi)/8=157.5^0`;
Area of the first rhombus`r_1=s^2*sintheta_1=9^2*sin15=20.96 sq.unit`
Area of the Second rhombus`r_2=s^2*sintheta_1=9^2*sin157.5=31.0 sq.unit :.`Difference between their areas `r_2-r_1=31.0-20.96=10.04sq.unit`[Ans]