Final answer:
The area of an equilateral triangle with a perimeter of 9 inches is 2.25√3 square inches, which does not match any of the provided multiple-choice options, indicating a potential error in the question.
Step-by-step explanation:
The subject is asking to find the area of an equilateral triangle with a perimeter of 9 inches. First, since an equilateral triangle has all sides of the same length, we take the total perimeter which is 9 inches and divide by 3, to find the length of one side, which is 3 inches. To find the area of an equilateral triangle, the formula is (√3/4) × side². Therefore, the area would be (√3/4) × 3², which simplifies to (√3/4) × 9. When you calculate the numerical value, it is 9√3/4 or effectively 9√3/4 square inches, which can be further simplified to 2.25√3 square inches. None of the multiple-choice options given, a) 9√3 b) 12√3 c) 18√3 d) 27√3, match the calculated value, suggesting a possible error in the question or in the provided options.