# Problem 18

Geometry Level 5

Given a pyramid $$SACB$$ with vertex $$S$$ whose base is a right triangle $$ACB$$ in which $$[ AB ]$$ is a hypotenuse with length $$2\sqrt3 \text{ cm}$$. The lateral edge $$[ SA ]$$ is perpendicular to the plane of the base. The dihedral angle formed by the lateral face $$SAC$$ and $$SAB$$ is $$30^\circ$$. The altitude of the pyramid is $$4\text{ cm}$$ in length. Find the lateral area.

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