Two rhombuses have sides with lengths of #5 #. If one rhombus has a corner with an angle of #(7pi)/12 # and the other has a corner with an angle of #(3pi)/8 #, what is the difference between the areas of the rhombuses?

Answer 1

Difference between the areas of the rhombuses is #0.525# sq. units.

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 #5# and angle #7pi/12# is

#1/2xx5^2xxsin(7pi/12)=1/2xx25xx0.966=12.075#

Hence area of rhombus with side #5# and angle #3pi/8# is

#1/2xx5^2xxsin(3pi/8)=1/2xx25xx0.924=11.55#

Difference between the areas of the rhombuses is #12.075-11.55=0.525#

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Answer 2

Carson Arnold

The difference between the areas of the two rhombuses is approximately (2.5\sqrt{3}) square units.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.