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

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Given two distinct points \(A\) and \(B\) in the plane, how many distinct points \(C\) are there on the same plane such that \(\triangle ABC\) is an equilateral triangle?

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There are \(8\) equilateral triangles each of which is \(4 \text{ cm}\) on a side. All of these triangles have been made by bending copper wires. Now, you unbend the wires and try to make squares with side length \(1 \text{ cm}.\) How many such squares can you make?

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

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