Answer: Perimeter = 6π ≈ 18.84
Area = 15π ≈ 47.10
Step-by-step explanation:
This is a composite of a big semicircle with diameter of 10 --> radius (r) = 5
plus a medium semicircle with diameter of 6 --> r = 3
minus a small semicircle with diameter of 4 --> r = 2
Perimeter of a semicircle = [tex]\dfrac{1}{2}(2\pi r)=\pi r[/tex]
[tex]P_{big}=\pi (5)\quad =5\pi\\P_{medium}=\pi (3)\quad =3\pi\\P_{small}=\pi (2)\quad =2\pi\\P_{composite} =5\pi+3\pi -2\pi\\.\qquad \qquad =\large\boxed{6\pi}[/tex]
Area of a semicircle = [tex]\dfrac{1}{2}(\pi r^2)[/tex]
[tex]A_{big}=\dfrac{1}{2}\pi (5)^2\quad =12.5\pi\\\\A_{medium}=\dfrac{1}{2}\pi (3)^2\quad =4.5\pi\\\\A_{small}=\dfrac{1}{2}\pi (2)^2\quad =2\pi\\\\A_{composite} =12.5\pi+4.5\pi -2\pi\\\\.\qquad \qquad =\large\boxed{15\pi}[/tex]
