To find the value of $y$, we need to recognize that the triangular face of the prism is a right triangle. In a right triangle, the Pythagorean theorem applies:

$c^2 = a^2 + b^2$

Where:

• $c$ is the hypotenuse (in this case, $y$),
• $a$ and $b$ are the other two sides of the triangle.

Given:

• One side $a = 9$ cm,
• The other side $b = 6$ cm.

Using the Pythagorean theorem:

$y^2 = 9^2 + 6^2$ $y^2 = 81 + 36$ $y^2 = 117$ $y = \sqrt{117}$

Simplifying $\sqrt{117}$:

$y \approx 10.82 \, \text{cm}$

So, the value of $y$ is approximately 10.82 cm.

Would you like to proceed with finding the surface area using this value of $y$, or do you have any further questions? Here are some related queries you may consider:

1. How does the value of $y$ affect the surface area of the prism?
2. What is the area of the triangular face now that $y$ is known?
3. How would you calculate the volume of the prism using the value of $y$?
4. Can the value of $y$ be expressed as a simplified radical?
5. What is the length of the hypotenuse in terms of the original dimensions?

Tip: When dealing with triangles, especially right triangles, the Pythagorean theorem is a crucial tool to remember for finding unknown sides.