Find the area of the kite in cm2? Round to 2 decimal places.

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1 Answer
CW
Apr 11, 2018

Area of the kite #=47.00 " cm"^2#

Explanation:

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Some properties of a kite :
a) The two diagonals are perpendicular, #=> AC and BD# are perpendicular.
b) the longer diagonal bisects the shorter one, #=> AO=OC=1/2AC#
As #AD=CD, and O# is the midpoint of #AC, OD# bisects #angleADC => angleODA=angleODC=34/2=17^@#
#=> OC=CDsin17^@~~3.5085# cm
#=> color(red)(AC=2*OC=2xx3.5085=7.017)# cm
#OD=12cos17~~11.4757# cm
#=> BO=sqrt(BC^2-OC^2)=sqrt(4^2-3.5085^2)=1.921# cm
#=> color(red)(BD=BO+OD=1.921+11.4757=13.3967)# cm
Area of the kite #= 1/2*AC*BD=1/2*7.017*13.3967=47.00 " cm"^2#

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