What is the area of the largest equilateral triangle which fits inside a square of side a?

so area of trinagle is $\frac{a^2}{2}$, however it is wrong, why ?

  • 1
    $\begingroup$ That's not an equilateral triangle, for one thing. $\endgroup$ Jan 27, 2017 at 18:43
  • 1
    $\begingroup$ The largest triangle is indeed half the area of the square. But the largest equilateral triangle will be something smaller than that. $\endgroup$
    – Doug M
    Jan 27, 2017 at 18:43
  • $\begingroup$ just get a piece of paper and draw a few pictures. This is a very visual problem. $\endgroup$
    – Will Jagy
    Jan 27, 2017 at 18:48
  • $\begingroup$ You shouldn't consider the height and the base to be equal, that is why the area isn't $\frac{a^2}{2}$ $\endgroup$
    – Seyed
    Jan 27, 2017 at 18:49
  • $\begingroup$ This provides an answer for triangles in general. $\endgroup$
    – Watson
    Jan 27, 2017 at 18:56

2 Answers 2


Hint. Place one vertex of the triangle on one of the corners of the square, and the other two vertices symmetrically placed on the opposite neighbouring sides of the square

  • $\begingroup$ ok what do i do after???????? $\endgroup$
    – user408113
    Jan 27, 2017 at 20:33
  • $\begingroup$ what do i do do do $\endgroup$
    – user408113
    Jan 27, 2017 at 21:00
  • $\begingroup$ Lanel the side of the triangle $x$ and use some basic trigonometry and Pythagoras to make an equation for $x$ $\endgroup$ Jan 27, 2017 at 21:01

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