The figure below was constructed by taking a semicircle with diameter 64 and replacing the diameter with four semicircles each having equal diameter. What is the perimeter of the figure?

![](https://cdn.mathpix.com/cropped/2024_04_17_2dbee4c747fee2855e37g-1.jpg?height=160&width=306&top_left_y=2143&top_left_x=969)
The length of a semicircular arc of diameter $d$ is half of the circumference of a circle of diameter $d$. Thus the length of a semicircular arc of diameter $d$ is $\frac{\pi d}{2}$.

Since the larger semicircle has diameter 64 units, this means the length of the large semicircular arc is $\frac{\pi d}{2}=\frac{64 \pi}{2}=32 \pi$.

The diameter of each small semicircle is $\frac{64}{4}=16$ units, so each small semicircular arc has length $\frac{16 \pi}{2}=8 \pi$.

There are four of these small arcs, so the perimeter of the figure is $32 \pi+4(8 \pi)=64 \pi$.

ANSWER: $64 \pi$