Two rhombuses have sides with lengths of #1 #. If one rhombus has a corner with an angle of #(pi)/2 # and the other has a corner with an angle of #(3pi)/8 #, what is the difference between the areas of the rhombuses?

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Answer 1 · 2016-03-16T15:55:16

The difference between areas of two rhombuses is #0.076#

Formula for area of a parallelogram with sides #a# and #b# and included angle #theta# is given by #axxbxxsintheta#

In a rhombus two sides are equal and as included angle is #theta# its area will be #a^2sintheta#.

Hence area of first rhombus is #1^2xxsin(pi/2)=1xx1=1#

Area of other rhombus is #1^2xxsin(3pi)/8=1xx0.924=0.924#

Hence the difference between areas of two rhombuses is #1-0.924=0.076#