Question

area of equilateral triangle with diagonal of 7?

Answer 1

Well the only diagonal of a triangle, is the side length itself,

So this means we have a triangle with all 3 sides equaling 7

The area of an equilateral triangle can be found using Weizenbock's principal that

\[\large A = \frac{a^2 + b^2 + c^2}{4\sqrt{3}}\]

Answer 2

It could be that "diagonal" refers to an altitude, median, or angle bisector, all of which are the same in an equilateral triangle. In that case you need only find the length of the base with some trigonometry:

\[\tan60^\circ=\frac{7}{x/2}=\frac{14}{x}\]
Then the area would be
\[A=\frac{1}{2}bh=\frac{7}{2}x\]