Bunuel wrote:

If the diagonal of a square of side √6 is the side of an equilateral triangle, what is the area of this triangle?

A. (3/8)·√3

B. (3/4)·√3

C. (3/2)·√3

D. 2·√6

E. 3·√3

The diagonal of a square is s√2, because the diagonal is the hypotenuse of a 45-45-90 triangle, with side ratio \(x: x : x\sqrt{2}\)

If square side is √6, its diagonal is √6 * √2 = √12

Side of equilateral triangle therefore is √12. Formula for area of equilateral triangle is

\(\frac{s^2\sqrt{3}}{4}\)

\(\frac{(√12)^2 * \sqrt{3}}{4}\) =

\(\frac{12\sqrt{3}}{4}\) =

3√3

Answer E If you don't know or don't remember the formula for the area of an equilateral triangle, draw its median (straight line from one vertex to opposite segment). The median of an equilateral triangle is a perpendicular bisector (of both angle and opposite side), and the altitude. You'll have two 30-60-90 triangles. Find the area of the equilateral triangle from there.

_________________

In the depths of winter, I finally learned

that within me there lay an invincible summer.

-- Albert Camus, "Return to Tipasa"