Public key cryptosystems using commutative algebra are not safe from quantum algorithm attacks. For this reason, experts have developed non-commutative algebra applied to geometry-based public key cryptosystems. This study develops a public key cryptosystem using the concept of geometry on the area of a triangle. We can show that the proposed public key cryptosystem works well. Furthermore, mathematical hacking experiments carried out by hackers are complex because the public key cryptosystem works on a ring of real numbers.