To estimate the area of an equilateral triangle, square its side, and then take a third and a tenth of the square. Why is this a very close approximation?
The answer is: for an equilateral triangle with side length \(a\), the
exact area is \(\dfrac{\sqrt{3}}{4}a^2\), where \(\dfrac{\sqrt{3}}{4} \approx 0.43301\), while \(\dfrac{1}{3} + \dfrac{1}{10} = \dfrac{13}{30} \approx 0.43333\)