To find the probability of picking a point in the shaded region, we need to calculate the area of the shaded region and the area of the entire shape (shaded plus unshaded region), then use the formula for probability:
\[ P(\text{shaded}) = \frac{\text{Area of shaded region}}{\text{Total area (shaded + unshaded)}} \]
Step 1: Find the area of the shaded region
The shaded region is made up of two right triangles. We use the formula for the area of a triangle, which is:
\[ \text{Area} = \frac{1}{2} \times \text{base} \times \text{height} \]
Area of the first triangle:
- Base = 14 cm
- Height = 25 cm
\[ \text{Area}_1 = \frac{1}{2} \times 14 \times 25 = \frac{1}{2} \times 350 = 175 \text{ cm}^2 \]
Area of the second triangle (since it is congruent, it will have the same area):
\[ \text{Area}_2 = 175 \text{ cm}^2 \]
Total area of the shaded region:
\[ \text{Area}_{\text{shaded}} = \text{Area}_1 + \text{Area}_2 = 175 + 175 = 350 \text{ cm}^2 \]
Step 2: Find the area of the unshaded region
The unshaded region consists of two right triangles, with one having a base of \(11\) cm and an unknown height. Let's assume each triangle has the same height.
Assuming the second unshaded triangle is also a right triangle and is congruent (for the sake of calculation), I will describe the unshaded area in pairs similarly:
Area of the unshaded triangle:
If we assume a simplified setup for calculation that the second unshaded triangle also has a base of \(11\) cm and has the same height (to simplify, let's assume this height to be equal to the earlier triangles or focus on the values given).
Let’s say:
- Both triangles base = 11 cm
- height can be assumed (since only one base is provided), but let’s just focus on \(2 * 11 = 22 \)
\[ \text{Area}_{\text{unshaded}} = \text{Area of base} = \frac{1}{2} \times 11 \times h = \frac{1}{2} \times 22 = \sum\text{2nd triangles}+ \sum\text{(Triangle incl.)} (dependant height); \]
Total area:
Let’s say we understand based heights correctly; you would ascertain Total Area from: \[ \text{Total Area} = \text{Shaded Area} + \text{Unshaded Area}; \] \[ = 350 + \text{sum} ; (h_{max}) \text { as congruent} \]
Putting it all together:
Total area units would yield \( \frac{\text{Area of shaded}}{\text{Area of unshaded}} = P_{shaded}\).
To find the probability of picking in shaded with drawn approximations:
Assuming properly, we can finalize with added figures where \(350 + 22 = 372\).
Finally the probability can yield:
\[ P(\text{shaded}) = \frac{350}{372} = 0.941 (round); \]
This could be \(0.94\) or \(0.95\), rounding respectively to the specified precision.
Thus the probability of picking a point in the shaded region, rounded to the nearest hundredth, is:
\[ \text{Probability} \approx 0.94 \text{ or nearby identical based on height input plausibilities.} \]
This would need conflict resolution on heights for clarity of output.