Find the perimeter of kite ABCD.?

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1 Answer
Douglas K.
Apr 4, 2018

Let #S' = AB = BC#

Let #S'' = CD = AD#

Using the Law of Cosines we can write these two equations:

#(36" ft")^2 = 2(S')^2-2(S')^2cos(80^@)#

#(36" ft")^2 = 2(S'')^2-2(S'')^2cos(40^@)#

#S' = sqrt(((36" ft")^2)/(2-2cos(80^@)))#

#S'' = sqrt(((36" ft")^2)/(2-2cos(40^@)))#

The perimeter is:

#P = 2S' + 2S''#

#P = 2sqrt(((36" ft")^2)/(2-2cos(80^@))) + 2sqrt(((36" ft")^2)/(2-2cos(40^@)))#

#P ~~ 161.26" ft"#

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