Answer:
(a) 44 cm
(b) 214 cm
Step-by-step explanation:
(a)
The figure perimeter it is half of a circle with a diameter d₁=14 cm and two halfs of circle with a diameter d₂=14 cm÷2=7 cm.
The length of a circle is L₀ = πd, where d is the diameter.
Therefore:
[tex]\bold{L=\frac12d_1+2\cdot\frac12d_2 = \frac12\cdot14\pi+\frac12\cdot2\cdot7\pi=14\pi\,cm\approx44\,cm}[/tex]
(b)
A full circle it is 360°, so the circle sector of 60° is [tex]\frac{60^o}{360^o}=\frac16[/tex] of the circle. So the arc of 60° is ¹/₆ of the full circle length.
The figure is an equilateral triangle and two 60°-sectors of circles with radiuses of length of the triangle's side (r=42 cm).
Its perimetr it's two radiuses, two arcs of 60° and one side of the triangle.
The length of a circle is L₀ = 2πr, where r is a radius.
Therefore:
[tex]\bold{L=2r+2\cdot\frac16\cdot 2\pi r+r=3r+\frac23\pi r}\\\\\bold{L=3\cdot42+\frac23\pi\cdot42=(126+28\pi)\,cm\approx214\,cm}[/tex]
