Let's analyze the image.

The area of the striped yellow triangle is given as 12 cm², and we are asked to calculate the area of the entire rectangle, which has a width of 3 cm.

To find the area of the rectangle, we will first need the formula for the area of a triangle:

$\text{Area of a triangle} = \frac{1}{2} \times \text{base} \times \text{height}$

The triangle is inside the rectangle, so its base is likely the same as the width of the rectangle, which is 3 cm. We are given the area of the triangle (12 cm²), so we can solve for the height of the triangle, which should be the same as the height of the rectangle.

Using the formula:

$12 = \frac{1}{2} \times 3 \times h$

Solving for $h$:

$12 = \frac{3}{2} \times h$

$h = \frac{12 \times 2}{3} = 8 \, \text{cm}$

Now that we know the height of the rectangle is 8 cm and the width is 3 cm, we can calculate the area of the rectangle:

$\text{Area of the rectangle} = \text{width} \times \text{height} = 3 \times 8 = 24 \, \text{cm}^2$

Thus, the area of the entire rectangle is 24 cm².

Would you like further details or have any questions?

Here are 5 related questions for further practice:

1. How would the area of the rectangle change if the width was doubled?
2. What would be the perimeter of the rectangle with the given dimensions?
3. How would you calculate the area if the rectangle were tilted by a certain angle?
4. If the green portion was a triangle, how would you calculate its area?
5. How could you find the diagonal length of the rectangle?

Tip: Always double-check the units used in area problems to avoid confusion.