Question

What is the answer to this??

Answer 1

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

$10^2=AD^2+5^2\\AD=\sqrt{100-25} \\AD=\sqrt{75}$

$AC=AD+DC=2\sqrt{75}=10\sqrt{3}$

$S=\frac{a^2\sqrt{3} }{4}$

$S=\frac{(10\sqrt{3})^2\sqrt{3} }{4} =\frac{300\sqrt{3} }{4} =75\sqrt{3} ft^2$

Answer: A) $S=75\sqrt{3}$ft²

P.S. Hello from Russia and sorry for my bad english :^)