An altitude of the triangle divides it into two right triangles, each with a leg of s/2 and a hypotenuse of 8s. Then the length of the altitude (h) is given by the Pythagorean theorem as ...
h² + (s/2)² = (8s)²
h = s√(64 -1/4) . . . . . . . subtract s²/4 and take the square root
Then the area is ...
A = (1/2)sh = (s/2)(s√63.75)
We can put all the constants in one place to get ...
