Peanut Perimeter

The circular arcs at the top and bottom are each ${\large\frac{3}{4}}$ of a circle with radius $2$ . The circumference of the whole circle is $4\pi$ , and so the length of each of these arcs is $3\pi$ .

The circular arcs at the left and right are each ${\large\frac{1}{4}}$ of a circle with radius $1$ . The circumference of the whole circle is $2\pi$ , and so the length of each of these arcs is ${\large\frac{\pi}{2}}$ .

The total perimeter is $7\pi$ .

If you know that $\pi\approx{\large\frac{22}{7}}$ , then it is easy to see that $7\pi\approx\boxed{22}$ . However, a calculation by hand will also show you that $7\times 3.14=21.98$ , which rounds to $\boxed{22}$ .

If anyone's curious, the area of the peanut is: $2\times(\frac{3}{4}\times\pi\times 2^{2}) + (9- \frac{1}{2}\times\pi\times 1^{2}) = 6\pi + 9 - \frac{1}{2}\pi \approx 26$

I did not read the problem at first and found the area instead of the perimeter! :P