Two rhombuses have sides with lengths of #4 #. If one rhombus has a corner with an angle of #pi/12 # and the other has a corner with an angle of #(5pi)/12 #, what is the difference between the areas of the rhombuses?

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Answer 1 · 2016-03-13T09:32:58

Difference in Area#=11.31372" "#square units

To compute the area of a rhombus
Use the formula
Area#=s^2*sin theta" "#where #s=#side of the rhombus and #theta=# angle between two sides

Compute the area of rhombus #1.#

Area#=4*4*sin ((5pi)/12)=16*sin 75^@=15.45482#
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Compute the area of rhombus #2.#

Area#=4*4*sin ((pi)/12)=16*sin 15^@=4.14110#
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Compute the difference in Area#=15.45482-4.14110=11.31372#

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