area-and-perimeter-of-circle-problem-solving-02

Answer: A

Area of shaded region = area of large circle − area of medium circle + area of small circle

\begin{equation*}
\begin{split}
\text{Area of shaded region}& = \pi\cdot 28^2 - \pi \cdot21^2 + \pi \cdot 7^2\\\\
\text{Area of shaded region}& = \frac{22}{7}\cdot 28^2 - \frac{22}{7}\cdot 21^2 + \frac{22}{7}\cdot 7^2\\\\
\text{Area of shaded region}& = 2464 - 1386 + 154\\\\
\text{Area of shaded region}& = 1232\text{ cm}^2
\end{split}
\end{equation*}

Perimeter of shaded region = circumference of large circle + circumference of medium circle + circumference of small circle

\begin{equation*}
\begin{split}
\text{Perimeter of shaded region} & = 2\cdot\pi \cdot 28 + 2\cdot \pi \cdot 21 + 2\cdot \pi \cdot7\\\\
\text{Perimeter of shaded region} & = 2\cdot \pi \times (28 + 21 + 7)\\\\
\text{Perimeter of shaded region} & = 2\cdot \frac{22}{7}\cdot 56\\\\
\text{Perimeter of shaded region} & = 352\text{ cm}
\end{split}
\end{equation*}