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:

enter image source here
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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