Answer:
(18π +4) cm ≈ 60.55 cm
Explanation:
You want the perimeter of a figure bounded by two semicircles and a straight line segment.
Perimeter
The perimeter of the figure is the sum of the lengths of the curves and lines that form its boundary. Here, one boundary is a semicircle of diameter 16 cm, another boundary is a semicircle of diameter 20 cm, and a straight line forms the remaining boundary.
Semicircles
The length of a semicircle is half the circumference of a full circle of the same diameter:
boundary length = 1/2(πd)
The smaller semicircle has a length of ...
boundary length (small) = 1/2π(16 cm) = 8π cm
The larger semicircle has a length of ...
boundary length [large] = 1/2π(20 cm) = 10π cm
Line segment
The length of the line segment is the difference of the diameters:
line segment length = (20 cm) -(16 cm) = 4 cm
Sum
The perimeter is the sum of these lengths:
P = boundary length (small) + boundary length (large) + line segment length
P = (8π +10π +4) cm = 18π +4 cm ≈ 60.55 cm
The perimeter of the figure is about 60.55 cm.
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Additional comment
The perimeter is closer to 60.549 cm, so rounds to 60.5 cm.