Uploaded July 2026 | Updated September 2026, 2 weeks ago

---

In this video, we explore whether the area of a 4‑gon can be determined using only the lengths of its four sides. Starting with this intriguing question, we move on to the area of a cyclic 4‑gon and then test the formula on familiar shapes like a rectangle and an isosceles trapezium. The lesson concludes with a generalization, highlighting special cases and showing how Heron’s formula for triangles is actually a special case of the generalized Brahmagupta formula for a 4‑gon.
Courses on Khan Academy are always 100% free. Start practicing and saving your progress now!
khanacademy.org/math/ncert-math-class-9-new/x56891bfac37feca0:measuring-space-perimeter-and-area

Timestamps:

00:00 Can we find the area of a 4-gon using only the lengths of its four sides?
01:26 Area of a cyclic 4-gon
02:33 Testing the formula on rectangle
03:26 Testing the formula on isosceles trapezium
07:33 Generalization and special case

Khan Academy India is a nonprofit organization with the mission of providing a free world-class education for anyone anywhere. We have videos and exercises that have been translated into multiple Indian languages and 15 million people around the globe learn on Khan Academy every month.
Support Us: india.khanacademy.org/donate