To find an expression for the perimeter of the given shape, we need to sum up all the side lengths. The perimeter $P$ is the sum of the lengths of all the sides.

From the image, the side lengths are labeled as:

• $3m^2 + 2$
• $12g^2$
• $7g + 4m$
• $5m^2$
• $8g$

The perimeter $P$ is:

$P = (3m^2 + 2) + (12g^2) + (7g + 4m) + (5m^2) + (8g)$

Now, let's combine like terms:

1. Combine the $m^2$ terms: $3m^2 + 5m^2 = 8m^2$

2. Combine the $g^2$ terms: $12g^2$

3. Combine the $g$ terms: $7g + 8g = 15g$

4. The constant term: $2$

Therefore, the simplified expression for the perimeter is:

$P = 8m^2 + 12g^2 + 15g + 4m + 2$

Would you like to delve deeper into the problem or have any other questions?

Here are 5 related questions for further exploration:

1. How would the expression for the perimeter change if one of the side lengths were doubled?
2. Can you calculate the perimeter if specific values for $m$ and $g$ were given?
3. What happens to the perimeter expression if the shape's sides are rearranged?
4. How would you express the perimeter if one of the $g^2$ terms was a negative value?
5. Can the expression for the perimeter be factored further?

Tip: When simplifying algebraic expressions, always group and simplify like terms first. This ensures the expression is in its simplest form.