Final answer:
The area of the rectangle is 96 cm², calculated by first determining the width to be 8 cm and the length to be 12 cm, using the given perimeter of 40 cm.
Step-by-step explanation:
To find the area of a rectangle when the length is 4 cm longer than its width, and the perimeter is 40 cm, we need to set up two equations. Let the width be w cm. Then the length is (w + 4) cm. The perimeter (P) of a rectangle is given by P = 2l + 2w, where l is the length and w is the width. Substituting our expressions for length and width, we get 40 = 2(w + 4) + 2w.
Simplify this to 40 = 2w + 8 + 2w and then to 40 = 4w + 8. Solving for w, we find that the width is w = (40 - 8) / 4, which is w = 8 cm. Therefore, the length is l = w + 4 = 12 cm.
Now, the area (A) of a rectangle is A = l × w. Substituting our values for length and width, the area of the rectangle is A = 12 cm × 8 cm, which is A = 96 cm².