The problem from the image states:

"A rectangular prism measures 2 cm by 2 cm by 5 cm. What is its surface area? Explain or show your reasoning."

Solution:

To calculate the surface area of a rectangular prism, we use the formula:

$\text{Surface Area} = 2(lw + lh + wh)$

Where:

• $l$ is the length,
• $w$ is the width,
• $h$ is the height.

Given:

• Length $l = 2 \, \text{cm}$,
• Width $w = 2 \, \text{cm}$,
• Height $h = 5 \, \text{cm}$.

Now, applying the values:

$\text{Surface Area} = 2(2 \times 2 + 2 \times 5 + 2 \times 5)$ $= 2(4 + 10 + 10)$ $= 2(24) = 48 \, \text{cm}^2$

Final Answer:

The surface area of the rectangular prism is $48 \, \text{cm}^2$.

Would you like further details or have any questions? Here are some related questions to expand your understanding:

1. How would the surface area change if the height was doubled?
2. Can you calculate the volume of the same rectangular prism?
3. What is the formula for the lateral surface area of a rectangular prism?
4. How do you find the surface area of a cube if all sides are equal?
5. What happens to the surface area if the dimensions are halved?

Tip: When working with surface area, ensure that all dimensions are in the same units before applying the formula!