Two rhombuses have sides with lengths of #7 #. 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 · 2017-06-05T22:37:00

#3,7299029069469489497190237195574...#

#pi/2#. a square. #A_1 = 49#

The other one, #A_2 = (d_1d_2)/2#

#d_1^2 = 7^2 + 7^2 - 2 * 7 * 7 * cos frac{3 pi}{8}#

So, #d_1 = 7,7779832622744311463996313952795#

#pi - (3 pi)/8 = (5pi)/8#

#d_2^2 = 7^2 + 7^2 - 2 * 7 * 7 * cos frac{5 pi}{8}#

So, #d_2 = 11,640574572235633319103037286651#

#A_2 - A_1 = 45,270097093053051050280976280443 - 49#