OFFICIAL EXPLANATION

Let AE be the perpendicular (Altitude) for both the triangles $$\mathrm{ABD} \& \mathrm{BDC}$$

As triangle BDC has all angles equal, it is an equilateral triangle, let each of its side be ' $$n$$ '
Next triangle $$A B D$$ is an isosceles triangle as angle $$D A B$$ is same as angle $$D B A$$, so we get $$A D=$$ $$B D=n$$ only (as $$B D$$ is also one of the sides of the equilateral triangle $$A D C$$ )

Thus, both the triangles $$\mathrm{ABD} \& \mathrm{BDC}$$ have equal altitude ( BE each) and equal length bases ( n each), it implies both the triangles are equal in area.

Hence column $$A$$ has same quantity as column $B$, so the answer is (C).