Two rhombuses have sides with lengths of #16 #. If one rhombus has a corner with an angle of #pi/12 # and the other has a corner with an angle of #(5pi)/6 #, what is the difference between the areas of the rhombuses?

1 Answer
Mar 20, 2016

Difference between the areas of the rhombuses is #30.848# sq.units.

Explanation:

Area of a parallelogram with sides #a# and #b# and included angle #theta# is given by #1/2xxaxxbxxsintheta#. As it is a rhombus, two sides are equal area will be #1/2xxa^2xxsintheta#.

Hence area of rhombus with side #16# and angle #pi/12# is

#1/2xx16^2xxsin(pi/12)=1/2xx256xx0.259=33.152#

Hence area of rhombus with side #16# and angle #5pi/6# is

#1/2xx16^2xxsin(5pi/6)=1/2xx256xx0.5=64#

Difference between the areas of the rhombuses is #64-33.152=30.848#