Hi @mirthfulcygnet,

Nice to hear from you! It is great that you are continuing to be interested and ask questions even after having finished the lessons!

It is true that there're exists a generalizations of Heron's Formula for quadrilaterals and pentagons, but they are much-much more complicated and oriented for higher-level mathematicians. The same relatively easy formulas for the areas of polygons with more than three angles, analogous to Heron's Formula, do not exist.

To begin with, Heron's formula is a special case of **Brahmagupta's formula** for the area of a **cyclic quadrilateral**. Brahmagupta's formula, in its turn, is a special case of **Bretschneider's formula** for the area of **any** quadrilateral.

Heron's formula is also a special case of the **formula** for the area of a **trapezoid** based only on its sides. Heron's formula is obtained by setting the smaller parallel side to zero.

One of the even more high-level formulas is a formula for Robbins pentagons: a cyclic pentagons whose side lengths and area are all rational numbers. If you really want to, you can read about it **here** (page 15), but I think it would be better for you to learn more in this area first. 🙂

Try to get used to the Heron's formula first and be ready to use it any time you need to! Then you will be ready to learn more such formulas.