Two rhombuses have sides with lengths of #13 #. If one rhombus has a corner with an angle of #(7pi)/8 # and the other has a corner with an angle of #(pi)/6 #, what is the difference between the areas of the rhombuses?

1 Answer
Mar 20, 2016

Difference between the areas of the rhombuses is #9.887# 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 #13# and angle #7pi/8# is

#1/2xx13^2xxsin7(pi/8)=1/2xx169xx0.383=32.363#

Hence area of rhombus with side #13# and angle #pi/6# is

#1/2xx13^2xxsin(pi/6)=1/2xx169xx0.5=42.25#

Difference between the areas of the rhombuses is #42.25-32.363=9.887#