HSG.C.B.5 math practice. Learn by doing.

This is a right triangle ($3$-$4$-$5$). Area $= \dfrac{1}{2} \times 3 \times 4 = 6$.

The area of the whole circle is $\pi r^{2} = \pi \cdot 6^{2} = 36\pi\textsf{.}$ A $90^{\circ}$ sector is $\dfrac{90}{360} = \dfrac{1}{4}$ of the circle, so the area is $\dfrac{1}{4} \cdot 36\pi = 9\pi\text{ m}^{2}\textsf{.}$

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 $\dfrac{1}{2} \cdot 10\pi = 5\pi\textsf{.}$

Area of a rhombus $= \dfrac{1}{2} \times d_{1} \times d_{2} = \dfrac{1}{2} \times 6 \times 8 = 24$.

The area of the whole circle is $\pi r^{2} = \pi \cdot 4^{2} = 16\pi\textsf{.}$ A $60^{\circ}$ sector is $\dfrac{60}{360} = \dfrac{1}{6}$ of the circle, so the area is $\dfrac{1}{6} \cdot 16\pi = \dfrac{8\pi}{3}\text{ in}^{2}\textsf{.}$

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

Area $= \dfrac{1}{2} \times 6 \times 8 = 24$.

The area of the whole circle is $\pi r^{2} = \pi \cdot 6^{2} = 36\pi\textsf{.}$ A $120^{\circ}$ sector is $\dfrac{120}{360} = \dfrac{1}{3}$ of the circle, so the area is $\dfrac{1}{3} \cdot 36\pi = 12\pi\text{ ft}^{2}\textsf{.}$