Perimeter and arc length. Game on.

The circumference is $2\pi r = 2\pi \cdot 5 = 10\pi\textsf{.}$ A $180^{\circ}$ arc is $\dfrac{180}{360} = \dfrac{1}{2}$ of the circle, so the arc length is $\dfrac{1}{2} \cdot 10\pi = 5\pi\textsf{.}$

$P = 7 + 10 + 12 = 29$.

The circumference is $2\pi r = 2\pi \cdot 6 = 12\pi\textsf{.}$ A $90^{\circ}$ arc is $\dfrac{90}{360} = \dfrac{1}{4}$ of the circle, so the arc length is $\dfrac{1}{4} \cdot 12\pi = 3\pi\textsf{.}$

$P = 2(15 + 6) = 2 \cdot 21 = 42$.

The circumference is $2\pi r = 2\pi \cdot 3 = 6\pi\textsf{.}$ A $180^{\circ}$ arc is $\dfrac{180}{360} = \dfrac{1}{2}$ of the circle, so the arc length is $\dfrac{1}{2} \cdot 6\pi = 3\pi\textsf{.}$

The circumference is $2\pi r = 2\pi \cdot 2 = 4\pi\textsf{.}$ A $90^{\circ}$ arc is $\dfrac{90}{360} = \dfrac{1}{4}$ of the circle, so the arc length is $\dfrac{1}{4} \cdot 4\pi = \pi\textsf{.}$

The circumference is $2\pi r = 2\pi \cdot 18 = 36\pi\textsf{.}$ A $30^{\circ}$ arc is $\dfrac{30}{360} = \dfrac{1}{12}$ of the circle, so the arc length is $\dfrac{1}{12} \cdot 36\pi = 3\pi\textsf{.}$

The circumference of the full circle is $2\pi r = 2\pi \cdot 10 = 20\pi\textsf{.}$ The curved edge is half of that, so $\dfrac{1}{2} \cdot 20\pi = 10\pi\textsf{.}$