The problem asks for the probability that a dart thrown at rectangle $ABCD$ will land in the shaded area, which is made up of two triangles inside the rectangle.

Steps to solve:

1. Calculate the area of the rectangle $ABCD$:

   • To find the total area of the rectangle, we need the lengths of sides $AB$ and $AD$.
   • Let's assume the rectangle has a width $w$ and height $h$, where $AB = w$ and $AD = h$.

2. Determine the area of the shaded triangles:

   • The shaded region consists of two right triangles, sharing one side with the diagonal $AC$.
   • The area of each right triangle is $\frac{1}{2} \times \text{base} \times \text{height}$.
   • Since both triangles are right triangles and their combined area makes up a part of the rectangle, we need to compute these areas precisely.

3. Calculate the probability:

   • Probability is the ratio of the shaded area to the total area of the rectangle: $P(\text{shaded}) = \frac{\text{Area of shaded region}}{\text{Area of rectangle}}$

Would you like to provide the dimensions of the rectangle or should I assume unit dimensions for a generic solution? Let me know if you'd like more details or if you have any specific dimensions in mind!

Relative Questions:

1. How do you calculate the area of a triangle in general?
2. What is the formula for the area of a rectangle?
3. How does probability relate to area in geometric probability problems?
4. What are the properties of right triangles that are useful in this scenario?
5. Can you apply this method to more complex shapes?

Tip: When working with geometric probabilities, always make sure to express the desired areas as fractions of the total region to simplify calculations!