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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