Explanation:
The equation given by Alexis to compute the area, A, of the deck is A=(15×17)+2(12×8×17). This simplifies to A=255+3264, which equals 3519.
The error that Alexis made in the equation is that she calculated the area of only the rectangular part of the deck (15 x 17), and then added twice the area of the triangular parts (2 x 12 x 8 x 17). However, this double-counts the area of the triangular portions, since they are already included in the rectangular part.
To correct the equation, we need to subtract the area of one of the triangular portions from the total. The deck is symmetrical, so we can calculate the area of one triangular portion as (1/2) x 12 x 8 = 48. Therefore, the correct equation for the area of the deck is:
A = (15 x 17) + 2(12 x 8 x 17) - 48
= 255 + 3264 - 48
= 3471
The correct area of the deck is 3471 square feet, not 3519 as originally calculated.