Problem: and are squares. Without invoking trigonometric functions, show that the area of triangle equals that of
Solution: Introducing a rectangular coordinate system and complex number
Let denote the area of triangle and respectively.
By Heron’s formula derived without invoking trigonometric function (see “An Algebraic Proof of Heron’s Formula“),
We also have
(see “Treasure Hunt with Complex Numbers“) and,
It is shown by Omega CAS Explorer that the expression under the square root of is the same as that of
Exercise-1 The two squares with area 25 and 36 ( see figure below) are positioned so that Find the area of triangle TSC.