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

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

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Answer 1 · 2018-04-11T03:50:55

Area of the kite $= 47.00 {cm}^{2}$ $=47.00 " cm"^2$

Explanation:

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Some properties of a kite :
a) The two diagonals are perpendicular, $\Rightarrow A C and B D$ $=> AC and BD$ are perpendicular.
b) the longer diagonal bisects the shorter one, $\Rightarrow A O = O C = \frac{1}{2} A C$ $=> AO=OC=1/2AC$
As $A D = C D, and O$ $AD=CD, and O$ is the midpoint of $A C, O D$ $AC, OD$ bisects $∠ A D C \Rightarrow ∠ O D A = ∠ O D C = \frac{34}{2} = 17^{\circ}$ $angleADC => angleODA=angleODC=34/2=17^@$
$\Rightarrow O C = C D {sin 17}^{\circ} \approx 3.5085$ $=> OC=CDsin17^@~~3.5085$ cm
$\Rightarrow A C = 2 \cdot O C = 2 \times 3.5085 = 7.017$ $=> color(red)(AC=2*OC=2xx3.5085=7.017)$ cm
$O D = 12 cos 17 \approx 11.4757$ $OD=12cos17~~11.4757$ cm
$\Rightarrow B O = \sqrt{B C^{2} - O C^{2}} = \sqrt{4^{2} - {3.5085}^{2}} = 1.921$ $=> BO=sqrt(BC^2-OC^2)=sqrt(4^2-3.5085^2)=1.921$ cm
$\Rightarrow B D = B O + O D = 1.921 + 11.4757 = 13.3967$ $=> color(red)(BD=BO+OD=1.921+11.4757=13.3967)$ cm
Area of the kite $= \frac{1}{2} \cdot A C \cdot B D = \frac{1}{2} \cdot 7.017 \cdot 13.3967 = 47.00 {cm}^{2}$ $= 1/2*AC*BD=1/2*7.017*13.3967=47.00 " cm"^2$

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

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