Question: Write an expression for the perimeter of this shape.
Simplify your answer fully.
$4f^2+3$
$7a$
$5f^2$
$11a^2$
$6a+2f$
Perimeter of the shape is the sum of all side lengths:
$(4f^2+3) + 7a + 5f^2 + (6a+2f) + 11a^2$
Simplified:
$11a^2 + 13a + 9f^2 + 2f + 3
1. **State the problem:** We need to find an expression for the perimeter of the shape by summing all given side lengths and then simplify the expression.
2. **Write the perimeter expression:** The perimeter $P$ is the sum of all sides:
$$P = (4f^2 + 3) + 7a + 5f^2 + (6a + 2f) + 11a^2$$
3. **Group like terms:** Group terms with $a^2$, $a$, $f^2$, $f$, and constants:
$$P = 11a^2 + (7a + 6a) + (4f^2 + 5f^2) + 2f + 3$$
4. **Simplify each group:**
- $7a + 6a = 13a$
- $4f^2 + 5f^2 = 9f^2$
So,
$$P = 11a^2 + 13a + 9f^2 + 2f + 3$$
5. **Final answer:** The simplified expression for the perimeter is:
$$\boxed{11a^2 + 13a + 9f^2 + 2f + 3}$$