Answer:
[tex]\sf Shaded \: Area=14 \pi r+49 \pi[/tex]
Step-by-step explanation:
Area of a circle
[tex]\sf A=\pi r^2 \quad \textsf{(where r is the radius)}[/tex]
To find the area of the shaded area, subtract the area of the unshaded circle from the larger circle.
Area of the larger circle
[tex]\implies \sf A=\pi (r+7)^2[/tex]
Area of the smaller (unshaded) circle
[tex]\implies \sf A=\pi r^2[/tex]
Therefore, the area of the shaded area is:
[tex]\implies \sf A=\pi (r+7)^2-\pi r^2[/tex]
Expand and simplify the expression:
[tex]\implies \sf A=\pi (r+7)^2-\pi r^2[/tex]
[tex]\implies \sf A=\pi (r^2+14r+49)-\pi r^2[/tex]
[tex]\implies \sf A=\pi r^2 +14 \pi r +49 \pi -\pi r^2[/tex]
[tex]\implies \sf A=14 \pi r+49 \pi[/tex]
