Answer: Perimeter = 8π ≈ 25.12
Area = 12π ≈ 37.68
Step-by-step explanation:
This is a composite of two figures.
The bigger figure is a quarter-circle with radius (r) = 8 cm
The smaller figure is a quarter-circle with diameter = 8 cm --> r = 4
Perimeter of a quarter-circle = [tex]\dfrac{1}{4}(2\pi r)[/tex] = [tex]\dfrac{\pi r}{2}[/tex]
Perimeter of composite figure = bigger - smaller figure
[tex]P_{bigger}=2\pi(8)\quad = 16\pi\\P_{smaller}=2\pi(4)\quad =8\pi\\P_{composite}=16\pi-8\pi \\.\qquad \qquad = \large\boxed{8\pi}[/tex]
Area of a quarter-circle = [tex]\dfrac{1}{4}\pi r^2[/tex]
[tex]A_{bigger}=\dfrac{1}{4}\pi (8)^2\quad =16\pi\\\\A_{smaller}=\dfrac{1}{4}\pi (4)^2\quad =4\pi\\\\A_{composite}=16\pi-4\pi\\.\qquad \qquad = \large\boxed{12\pi}[/tex]
