To find the area of the rectangle, we first need to determine its width.

The formula for the perimeter $P$ of a rectangle is: $P = 2L + 2W$ where $L$ is the length, and $W$ is the width.

Given:

• The perimeter $P = 40$ cm
• The length $L = 12$ cm

Substituting these values into the formula: $40 = 2(12) + 2W$ Simplifying: $40 = 24 + 2W$ Subtract 24 from both sides: $16 = 2W$ Now, divide by 2: $W = 8 \, \text{cm}$

Now that we have both the length and the width, we can find the area $A$ of the rectangle using the formula: $A = L \times W$ Substituting the values: $A = 12 \times 8 = 96 \, \text{cm}^2$

Thus, the area of the rectangle is $96 \, \text{cm}^2$.

Would you like further details or have any questions?

Here are some related questions to explore:

1. What would the area be if the length was doubled?
2. How does the area change if the perimeter increases by 10 cm?
3. How do you find the diagonal of this rectangle?
4. If the width was unknown, how would you solve for it using the perimeter formula?
5. What is the difference in area between this rectangle and one with a perimeter of 50 cm?

Tip: To find unknown dimensions of a rectangle, knowing the perimeter or area is key to setting up useful equations.