Answer
$\frac{\sqrt{3}~s^2}{4}$
Work Step by Step
We can draw a perpendicular line from the top of the triangle to the base of the triangle that makes two $30^{\circ}-60^{\circ}$ triangles. We know that the lengths of the sides of these triangles have the ratio $1, \sqrt{3},$ and $2$.
In this case, the sides are $\frac{s}{2}, \frac{\sqrt{3}~s}{2},$ and $s$.
The area of one of these triangles is $\frac{1}{2}bh$.
$A = \frac{1}{2}bh$
$A = \frac{1}{2}(\frac{s}{2})(\frac{\sqrt{3}~s}{2})$
$A = \frac{\sqrt{3}s^2}{8}$
Since there are two $30^{\circ}-60^{\circ}$ triangles, the total area is $2\times \frac{\sqrt{3}~s^2}{8}$ which is $\frac{\sqrt{3}~s^2}{4}$
The area of this equilateral triangle is $\frac{\sqrt{3}~s^2}{4}$
