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If the perimeter is 9 inches, each side is 3 inches.
The height of an equilateral triangle splits the triangle in two right sub-triangles: for example, consider a triangle ABC and the height AH starting from A, perpendicular to BC.
The triangle AHC is a right triangle, whose legs are AH and HC, and whose hypotenuse is AC.
AH is half the side, and AC is a side. So, we can use the Pythagorean theorem to find the height:
So, the area is