In triunghiul DAC:
AD = AC cos DAC
AC = AD ÷ cos DAC
AC = 6 × 2 = 12 cm
CD = AC sin DAC =
[tex]12 \times \frac{ \sqrt{3} }{2} = 6 \sqrt{3} [/tex]
In triunghiul DAB:
m(DAB) = 90 - 60 = 30
AD = AB cos DAB
AB = AD ÷ cos DAB =
[tex] \frac{6}{ \frac{ \sqrt{3} }{2} } = \frac{12}{ \sqrt{3} } = \frac{12 \sqrt{3} }{3} = 4 \sqrt{3} [/tex]
BD = AB sin DAB =
[tex]4 \sqrt{3} \times \frac{1}{2} = 2 \sqrt{3} [/tex]
[tex]P_{ABC}= AB + AC + BD + CD = 4\sqrt{3}+12+2\sqrt{3}+6\sqrt{3}=12 + 12\sqrt{3}[/tex]
