Since the triangle is equilateral, all its angles are equal to 60°
AO is the bisector⇒∠OAD = 30°
AO AO is the hypotenuse, ∠OAD = 30°⇒
OD=10:2=5ft
By the Pythagorean theorem
[tex]10^2=AD^2+5^2\\AD=\sqrt{100-25} \\AD=\sqrt{75}[/tex]
[tex]AC=AD+DC=2\sqrt{75}=10\sqrt{3}[/tex]
[tex]S=\frac{a^2\sqrt{3} }{4}[/tex]
[tex]S=\frac{(10\sqrt{3})^2\sqrt{3} }{4} =\frac{300\sqrt{3} }{4} =75\sqrt{3} ft^2[/tex]
Answer: A) [tex]S=75\sqrt{3}[/tex]ft²
P.S. Hello from Russia and sorry for my bad english :^)
