Geometry
# Classification of Triangles

$\angle ABC=60^\circ$ and $\angle ACB=60^\circ.$ If $\lvert \overline{AB}\rvert =3,$ what is the area of $\triangle ABC$?

In the above diagram,$\triangle ABC$ is $a=3.$ If $D$ is the midpoint of $\overline{BC}$ and $\triangle ADE$ is also an equilateral triangle, what is the area of $\triangle ABE$?

In the above diagram, the side length of equilateral triangle$\overline{AB}=5.$ What is the height of $\triangle ABC$?

In the above diagram, the triangle is the equilateral triangle. If