Solution:

The problem involves calculating the area of the shaded triangle within the rectangle $CDEF$.

Step 1: Understand the given information

• $CDEF$ is a rectangle with an area of $24 \, \text{ft}^2$.
• The length of side $CD$ is $6 \, \text{ft}$.
• The length of side $CF$ (height of the rectangle) can be calculated using the area of the rectangle: $\text{Area of Rectangle} = \text{Length} \times \text{Width} \implies 24 = 6 \times \text{Width}.$ Solving for $\text{Width}$: $\text{Width} = 4 \, \text{ft}.$

Thus, $CF = 4 \, \text{ft}$.

Step 2: Dimensions of the shaded triangle

The shaded part is a right triangle with:

• Base $CF = 3 \, \text{ft}$ (from $C$ to $F$),
• Height $CD = 3 \, \text{ft}$.

Step 3: Calculate the area of the shaded triangle

The formula for the area of a triangle is: $\text{Area of Triangle} = \frac{1}{2} \times \text{Base} \times \text{Height}.$ Substitute the values: $\text{Area of Shaded Triangle} = \frac{1}{2} \times 3 \times 3 = \frac{9}{2} = 4.5 \, \text{ft}^2.$

Final Answer:

The area of the shaded part is: $\boxed{4.5 \, \text{ft}^2}.$

Let me know if you would like further clarification or assistance!

Additional Questions:

1. What is the area of the remaining triangle in the rectangle?
2. How does the formula for the area of a triangle apply in similar problems?
3. What if the base or height of the triangle was extended? How would the area change?
4. Can you find the perimeter of the triangle if needed?
5. What if the rectangle had a different orientation—would the shaded area formula still apply?

Tip:

Always label and double-check your dimensions before calculating areas, especially in composite shapes!