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

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Answer 1 · 2016-03-13T10:13:49

Difference between the areas#=9.56709-6.47048=3.09661#

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#=5*5*sin ((pi)/8)=25*sin 22.5^@=9.56709#
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Compute the area of rhombus #2.#

Area#=5*5*sin ((pi)/12)=25*sin 15^@=6.47048#
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Compute the difference in Area#=9.56709-6.47048=3.09661#

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