Which square should be added to the area model of x²+18x to make a complete square?

Correct answer: A square of area 81

The direct answer is C: a square of area 81. Split the 18x term into two equal rectangles, each with area 9x. Each rectangle can have side lengths x and 9. To complete the large square, the missing corner must then be a 9 by 9 square, whose area is 9²=81. Algebraically, x²+18x+81=(x+9)². Option A uses 18 directly and does not create two 9x rectangles. Option B squares 6, but half of 18 is 9, not 6. Option C correctly uses half the coefficient of x and squares it. Option D squares 18, which is much too large and corresponds to the common mistake of forgetting the half-step. Memory cue: for x²+bx, add (b/2)²; here (18/2)²=9²=81.