diff --git a/geometry/geometry.py b/geometry/geometry.py
index a0be8eb3befc..aa3f57f78c19 100644
--- a/geometry/geometry.py
+++ b/geometry/geometry.py
@@ -103,9 +103,12 @@ def area(self) -> float:
     def perimeter(self) -> float:
         """
         >>> Ellipse(5, 10).perimeter
-        47.12388980384689
+        48.44210548835644
         """
-        return math.pi * (self.major_radius + self.minor_radius)
+        a, b = self.major_radius, self.minor_radius
+        # Use Ramanujan's first approximation for ellipse perimeter
+        # https://en.wikipedia.org/wiki/Perimeter_of_an_ellipse#First_approximation
+        return math.pi * (3 * (a + b) - ((3 * a + b) * (a + 3 * b)) ** 0.5)
 
 
 class Circle(Ellipse):