Question

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

Answer 1

Difference in areas `=38.8612`

Explanation:

Rhombus (1)
Side = 8 & `/_(pi/12)`
`sin(pi/12)=(h1)/8`
`h1=8*sin(pi/12)=2.0706`
Area of Rhombus (1) `=8*(h1)=8*2.0706=16.5644`

Rhombus (2)
Side = 8, `/_(pi/3)`
`h2=8*sin(pi/3)=(8*sqrt3)/2=4sqrt3=6.9282`
Area of Rhombus (2) `=8*6.9282=55.4256`
Difference in areas `=55.4256-16.5644=38.8612`