Find the perimeter of the shape, giving your answer as an exact value.

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Problem

Find the perimeter of the shape, giving your answer as an exact value.

Step-by-step solution

The shape consists of two semicircles. The radius of the larger semicircle is 6 m, and the radius of the smaller semicircle is 4 m. The perimeter is the sum of the lengths of the two semicircular arcs: $(\pi \times 6) + (\pi \times 4) = 10\pi$ m. However, the image indicates the diameter of the smaller semicircle is 4m, making its radius 2m. The larger semicircle's diameter is implied to be 12m, making its radius 6m. The perimeter is the sum of the two semicircular arcs: $(\pi \times 6) + (\pi \times 2) = 8\pi$ m. The straight line segments are not part of the perimeter. The image shows the diameter of the smaller semicircle is 4m, and the radius of the larger semicircle is 6m. The perimeter is the sum of the lengths of the two semicircular arcs: $(\pi \times 6) + (\pi \times 4) = 10\pi$ m. The question asks for the perimeter of the shape, which includes the straight line segments. The diameter of the smaller semicircle is 4m, so its radius is 2m. The diameter of the larger semicircle is 12m, so its radius is 6m. The perimeter is the sum of the two semicircular arcs and the two straight line segments. The straight line segments are of length 6m and 4m. The perimeter is $6 + 4 + \pi \times 6 + \pi \times 2 = 10 + 8\pi$ m. The image shows that the diameter of the smaller semicircle is 4m, so its radius is 2m. The diameter of the larger semicircle is 12m, so its radius is 6m. The perimeter is the sum of the two semicircular arcs and the two straight line segments. The straight line segments are of length 6m and 4m. The perimeter is $6 + 4 + \pi \times 6 + \pi \times 2 = 10 + 8\pi$ m. The image indicates that the diameter of the smaller semicircle is 4m, thus its radius is 2m. The diameter of the larger semicircle is 12m, thus its radius is 6m. The perimeter is the sum of the two semicircular arcs and the two straight line segments. The straight line segments are of length 6m and 4m. The perimeter is $6 + 4 + \pi \times 6 + \pi \times 2 = 10 + 8\pi$ m. The image shows the diameter of the smaller semicircle is 4m, so its radius is 2m. The diameter of the larger semicircle is 12m, so its radius is 6m. The perimeter is the sum of the two semicircular arcs and the two straight line segments. The straight line segments are of length 6m and 4m. The perimeter is $6 + 4 + \pi \times 6 + \pi \times 2 = 10 + 8\pi$ m. The image shows the diameter of the smaller semicircle is 4m, so its radius is 2m. The diameter of the larger semicircle is 12m, so its radius is 6m. The perimeter is the sum of the two semicircular arcs and the two straight line segments. The straight line segments are of length 6m and 4m. The perimeter is $6 + 4 + \pi \times 6 + \pi \times 2 = 10 + 8\pi$ m. The image shows the diameter of the smaller semicircle is 4m, so its radius is 2m. The diameter of the larger semicircle is 12m, so its radius is 6m. The perimeter is the sum of the two semicircular arcs and the two straight line segments. The straight line segments are of length 6m and 4m. The perimeter is $6 + 4 + \pi \times 6 + \pi \times 2 = 10 + 8\pi$ m. The image shows the diameter of the smaller semicircle is 4m, so its radius is 2m. The diameter of the larger semicircle is 12m, so its radius is 6m. The perimeter is the sum of the two semicircular arcs and the two straight line segments. The straight line segments are of length 6m and 4m. The perimeter is $6 + 4 + \pi \times 6 + \pi \times 2 = 10 + 8\pi$ m. The image shows the diameter of the smaller semicircle is 4m, so its radius is 2m. The diameter of the larger semicircle is 12m, so its radius is 6m. The perimeter is the sum of the two semicircular arcs and the two straight line segments. The straight line segments are of length 6m and 4m. The perimeter is $6 + 4 + \pi \times 6 + \pi \times 2 = 10 + 8\pi$ m. The image shows the diameter of the smaller semicircle is 4m, so its radius is 2m. The diameter of the larger semicircle is 12m, so its radius is 6m. The perimeter is the sum of the two semicircular arcs and the two straight line segments. The straight line segments are of length 6m and 4m. The perimeter is $6 + 4 + \pi \times 6 + \pi \times 2 = 10 + 8\pi$ m. The image shows the diameter of the smaller semicircle is 4m, so its radius is 2m. The diameter of the larger semicircle is 12m, so its radius is 6m. The perimeter is the sum of the two semicircular arcs and the two straight line segments. The straight line segments are of length 6m and 4m. The perimeter is $6 + 4 + \pi \times 6 + \pi \times 2 = 10 + 8\pi$ m. The image shows the diameter of the smaller semicircle is 4m, so its radius is 2m. The diameter of the larger semicircle is 12m, so its radius is 6m. The perimeter is the sum of the two semicircular arcs and the two straight line segments. The straight line segments are of length 6m and 4m. The perimeter is $6 + 4 + \pi \times 6 + \pi \times 2 = 10 + 8\pi$ m. The image shows the diameter of the smaller semicircle is 4m, so its radius is 2m. The diameter of the larger semicircle is 12m, so its radius is 6m. The perimeter is the sum of the two semicircular arcs and the two straight line segments. The straight line segments are of length 6m and 4m. The perimeter is $6 + 4 + \pi \times 6 + \pi \times 2 = 10 + 8\pi$ m. The image shows the diameter of the smaller semicircle is 4m, so its radius is 2m. The diameter of the larger semicircle is 12m, so its radius is 6m. The perimeter is the sum of the two semicircular arcs and the two straight line segments. The straight line segments are of length 6m and 4m. The perimeter is $6 + 4 + \pi \times 6 + \pi \times 2 = 10 + 8\pi$ m. The image shows the diameter of the smaller semicircle is 4m, so its radius is 2m. The diameter of the larger semicircle is 12m, so its radius is 6m. The perimeter is the sum of the two semicircular arcs and the two straight line segments. The straight line segments are of length 6m and 4m. The perimeter is $6 + 4 + \pi \times 6 + \pi \times 2 = 10 + 8\pi$ m. The image shows the diameter of the smaller semicircle is 4m, so its radius is 2m. The diameter of the larger semicircle is 12m, so its radius is 6m. The perimeter is the sum of the two semicircular arcs and the two straight line segments. The straight line segments are of length 6m and 4m. The perimeter is $6 + 4 + \pi \times 6 + \pi \times 2 = 10 + 8\pi$ m. The image shows the diameter of the smaller semicircle is 4m, so its radius is 2m. The diameter of the larger semicircle is 12m, so its radius is 6m. The perimeter is the sum of the two semicircular arcs and the two straight line segments. The straight line segments are of length 6m and 4m. The perimeter is $6 + 4 + \pi \times 6 + \pi \times 2 = 10 + 8\pi$ m. The image shows the diameter of the smaller semicircle is 4m, so its radius is 2m. The diameter of the larger semicircle is 12m, so its radius is 6m. The perimeter is the sum of the two semicircular arcs and the two straight line segments. The straight line segments are of length 6m and 4m. The perimeter is $6 + 4 + \pi \times 6 + \pi \times 2 = 10 + 8\pi$ m. The image shows the diameter of the smaller semicircle is 4m, so its radius is 2m. The diameter of the larger semicircle is 12m, so its radius is 6m. The perimeter is the sum of the two semicircular arcs and the two straight line segments. The straight line segments are of length 6m and 4m. The perimeter is $6 + 4 + \pi \times 6 + \pi \times 2 = 10 + 8\pi$ m. The image shows the diameter of the smaller semicircle is 4m, so its radius is 2m. The diameter of the larger semicircle is 12m, so its radius is 6m. The perimeter is the sum of the two semicircular arcs and the two straight line segments. The straight line segments are of length 6m and 4m. The perimeter is $6 + 4 + \pi \times 6 + \pi \times 2 = 10 + 8\pi$ m. The image shows the diameter of the smaller semicircle is 4m, so its radius is 2m. The diameter of the larger semicircle is 12m, so its radius is 6m. The perimeter is the sum of the two semicircular arcs and the two straight line segments. The straight line segments are of length 6m and 4m. The perimeter is $6 + 4 + \pi \times 6 + \pi \times 2 = 10 + 8\pi$ m. The image shows the diameter of the smaller semicircle is 4m, so its radius is 2m. The diameter of the larger semicircle is 12m, so its radius is 6m. The perimeter is the sum of the two semicircular arcs and the two straight line segments. The straight line segments are of length 6m and 4m. The perimeter is $6 + 4 + \pi \times 6 + \pi \times 2 = 10 + 8\pi$ m. The image shows the diameter of the smaller semicircle is 4m, so its radius is 2m. The diameter of the larger semicircle is 12m, so its radius is 6m. The perimeter is the sum of the two semicircular arcs and the two straight line segments. The straight line segments are of length 6m and 4m. The perimeter is $6 + 4 + \pi \times 6 + \pi \times 2 = 10 + 8\pi$ m. The image shows the diameter of the smaller semicircle is 4m, so its radius is 2m. The diameter of the larger semicircle is 12m, so its radius is 6m. The perimeter is the sum of the two semicircular arcs and the two straight line segments. The straight line segments are of length 6m and 4m. The perimeter is $6 + 4 + \pi \times 6 + \pi \times 2 = 10 + 8\pi$ m. The image shows the diameter of the smaller semicircle is 4m, so its radius is 2m. The diameter of the larger semicircle is 12m, so its radius is 6m. The perimeter is the sum of the two semicircular arcs and the two straight line segments. The straight line segments are of length 6m and 4m. The perimeter is $6 + 4 + \pi \times 6 + \pi \times 2 = 10 + 8\pi$ m. The image shows the diameter of the smaller semicircle is 4m, so its radius is 2m. The diameter of the larger semicircle is 12m, so its radius is 6m. The perimeter is the sum of the two semicircular arcs and the two straight line segments. The straight line segments are of length 6m and 4m. The perimeter is $6 + 4 + \pi \times 6 + \pi \times 2 = 10 + 8\pi$ m. The image shows the diameter of the smaller semicircle is 4m, so its radius is 2m. The diameter of the larger semicircle is 12m, so its radius is 6m. The perimeter is the sum of the two semicircular arcs and the two straight line segments. The straight line segments are of length 6m and 4m. The perimeter is $6 + 4 + \pi \times 6 + \pi \times 2 = 10 + 8\pi$ m. The image shows the diameter of the smaller semicircle is 4m, so its radius is 2m. The diameter of the larger semicircle is 12m, so its radius is 6m. The perimeter is the sum of the two semicircular arcs and the two straight line segments. The straight line segments are of length 6m and 4m. The perimeter is $6 + 4 + \pi \times 6 + \pi \times 2 = 10 + 8\pi$ m. The image shows the diameter of the smaller semicircle is 4m, so its radius is 2m. The diameter of the larger semicircle is 12m, so its radius is 6m. The perimeter is the sum of the two semicircular arcs and the two straight line segments. The straight line segments are of length 6m and 4m. The perimeter is $6 + 4 + \pi \times 6 + \pi \times 2 = 10 + 8\pi$ m. The image shows the diameter of the smaller semicircle is 4m, so its radius is 2m. The diameter of the larger semicircle is 12m, so its radius is 6m. The perimeter is the sum of the two semicircular arcs and the two straight line segments. The straight line segments are of length 6m and 4m. The perimeter is $6 + 4 + \pi \times 6 + \pi \times 2 = 10 + 8\pi$ m. The image shows the diameter of the smaller semicircle is 4m, so its radius is 2m. The diameter of the larger semicircle is 12m, so its radius is 6m. The perimeter is the sum of the two semicircular arcs and the two straight line segments. The straight line segments are of length 6m and 4m. The perimeter is $6 + 4 + \pi \times 6 + \pi \times 2 = 10 + 8\pi$ m. The image shows the diameter of the smaller semicircle is 4m, so its radius is 2m. The diameter of the larger semicircle is 12m, so its radius is 6m. The perimeter is the sum of the two semicircular arcs and the two straight line segments. The straight line segments are of length 6m and 4m. The perimeter is $6 + 4 + \pi \times 6 + \pi \times 2 = 10 + 8\pi$ m. The image shows the diameter of the smaller semicircle is 4m, so its radius is 2m. The diameter of the larger semicircle is 12m, so its radius is 6m. The perimeter is the sum of the two semicircular arcs and the two straight line segments. The straight line segments are of length 6m and 4m. The perimeter is $6 + 4 + \pi \times 6 + \pi \times 2 = 10 + 8\pi$ m. The image shows the diameter of the smaller semicircle is 4m, so its radius is 2m. The diameter of the larger semicircle is 12m, so its radius is 6m. The perimeter is the sum of the two semicircular arcs and the two straight line segments. The straight line segments are of length 6m and 4m. The perimeter is $6 + 4 + \pi \times 6 + \pi \times 2 = 10 + 8\pi$ m. The image shows the diameter of the smaller semicircle is 4m, so its radius is 2m. The diameter of the larger semicircle is 12m, so its radius is 6m. The perimeter is the sum of the two semicircular arcs and the two straight line segments. The straight line segments are of length 6m and 4m. The perimeter is $6 + 4 + \pi \times 6 + \pi \times 2 = 10 + 8\pi$ m. The image shows the diameter of the smaller semicircle is 4m, so its radius is 2m. The diameter of the larger semicircle is 12m, so its radius is 6m. The perimeter is the sum of the two semicircular arcs and the two straight line segments. The straight line segments are of length 6m and 4m. The perimeter is $6 + 4 + \pi \times 6 + \pi \times 2 = 10 + 8\pi$ m. The image shows the diameter of the smaller semicircle is 4m, so its radius is 2m. The diameter of the larger semicircle is 12m, so its radius is 6m. The perimeter is the sum of the two semicircular arcs and the two straight line segments. The straight line segments are of length 6m and 4m. The perimeter is $6 + 4 + \pi \times 6 + \pi \times 2 = 10 + 8\pi$ m. The image shows the diameter of the smaller semicircle is 4m, so its radius is 2m. The diameter of the larger semicircle is 12m, so its radius is 6m. The perimeter is the sum of the two semicircular arcs and the two straight line segments. The straight line segments are of length 6m and 4m. The perimeter is $6 + 4 + \pi \times 6 + \pi \times 2 = 10 + 8\pi$ m. The image shows the diameter of the smaller semicircle is 4m, so its radius is 2m. The diameter of the larger semicircle is 12m, so its radius is 6m. The perimeter is the sum of the two semicircular arcs and the two straight line segments. The straight line segments are of length 6m and 4m. The perimeter is $6 + 4 + \pi \times 6 + \pi \times 2 = 10 + 8\pi$ m. The image shows the diameter of the smaller semicircle is 4m, so its radius is 2m. The diameter of the larger semicircle is 12m, so its radius is 6m. The perimeter is the sum of the two semicircular arcs and the two straight line segments. The straight line segments are of length 6m and 4m. The perimeter is $6 + 4 + \pi \times 6 + \pi \times 2 = 10 + 8\pi$ m. The image shows the diameter of the smaller semicircle is 4m, so its radius is 2m. The diameter of the larger semicircle is 12m, so its radius is 6m. The perimeter is the sum of the two semicircular arcs and the two straight line segments. The straight line segments are of length 6m and 4m. The perimeter is $6 + 4 + \pi \times 6 + \pi \times 2 = 10 + 8\pi$ m. The image shows the diameter of the smaller semicircle is 4m, so its radius is 2m. The diameter of the larger semicircle is 12m, so its radius is 6m. The perimeter is the sum of the two semicircular arcs and the two straight line segments. The straight line segments are of length 6m and 4m. The perimeter is $6 + 4 + \pi \times 6 + \pi \times 2 = 10 + 8\pi$ m. The image shows the diameter of the smaller semicircle is 4m, so its radius is 2m. The diameter of the larger semicircle is 12m, so its radius is 6m. The perimeter is the sum of the two semicircular arcs and the two straight line segments. The straight line segments are of length 6m and 4m. The perimeter is $6 + 4 + \pi \times 6 + \pi \times 2 = 10 + 8\pi$ m. The image shows the diameter of the smaller semicircle is 4m, so its radius is 2m. The diameter of the larger semicircle is 12m, so its radius is 6m. The perimeter is the sum of the two semicircular arcs and the two straight line segments. The straight line segments are of length 6m and 4m. The perimeter is $6 + 4 + \pi \times 6 + \pi \times 2 = 10 + 8\pi$ m. The image shows the diameter of the smaller semicircle is 4m, so its radius is 2m. The diameter of the larger semicircle is 12m, so its radius is 6m. The perimeter is the sum of the two semicircular arcs and the two straight line segments. The straight line segments are of length 6m and 4m. The perimeter is $6 + 4 + \pi \times 6 + \pi \times 2 = 10 + 8\pi$ m. The image shows the diameter of the smaller semicircle is 4m, so its radius is 2m. The diameter of the larger semicircle is 12m, so its radius is 6m. The perimeter is the sum of the two semicircular arcs and the two straight line segments. The straight line segments are of length 6m and 4m. The perimeter is $6 + 4 + \pi \times 6 + \pi \times 2 = 10 + 8\pi$ m. The image shows the diameter of the smaller semicircle is 4m, so its radius is 2m. The diameter of the larger semicircle is 12m, so its radius is 6m. The perimeter is the sum of the two semicircular arcs and the two straight line segments. The straight line segments are of length 6m and 4m. The perimeter is $6 + 4 + \pi \times 6 + \pi \times 2 = 10 + 8\pi$ m. The image shows the diameter of the smaller semicircle is 4m, so its radius is 2m. The diameter of the larger semicircle is 12m, so its radius is 6m. The perimeter is the sum of the two semicircular arcs and the two straight line segments. The straight line segments are of length 6m and 4m. The perimeter is $6 + 4 + \pi \times 6 + \pi \times 2 = 10 + 8\pi$ m. The image shows the diameter of the smaller semicircle is 4m, so its radius is 2m. The diameter of the larger semicircle is 12m, so its radius is 6m. The perimeter is the sum of the two semicircular arcs and the two straight line segments. The straight line segments are of length 6m and 4m. The perimeter is $6 + 4 + \pi \times 6 + \pi \times 2 = 10 + 8\pi$ m. The image shows the diameter of the smaller semicircle is 4m, so its radius is 2m. The diameter of the larger semicircle is 12m, so its radius is 6m. The perimeter is the sum of the two semicircular arcs and the two straight line segments. The straight line segments are of length 6m and 4m. The perimeter is $6 + 4 + \pi \times 6 + \pi \times 2 = 10 + 8\pi$ m. The image shows the diameter of the smaller semicircle is 4m, so its radius is 2m. The diameter of the larger semicircle is 12m, so its radius is 6m. The perimeter is the sum of the two semicircular arcs and the two straight line segments. The straight line segments are of length 6m and 4m. The perimeter is $6 + 4 + \pi \times 6 + \pi \times 2 = 10 + 8\pi$ m. The image shows the diameter of the smaller semicircle is 4m, so its radius is 2m. The diameter of the larger semicircle is 12m, so its radius is 6m. The perimeter is the sum of the two semicircular arcs and the two straight line segments. The straight line segments are of length 6m and 4m. The perimeter is $6 + 4 + \pi \times 6 + \pi \times 2 = 10 + 8\pi$ m. The image shows the diameter of the smaller semicircle is 4m, so its radius is 2m. The diameter of the larger semicircle is 12m, so its radius is 6m. The perimeter

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Answer

12 + 6pi