2026 AMC 8 Problem 11

Attempt Problem 11 of the 2026 AMC 8 below, then check your answer against the video solution and professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2026 AMC 8 solutions, or check the answer key.

All problems are used with official legal permission of the Mathematical Association of America (MAA).

11.

Squares of side length 1,1, 1,1, 2,2, 3,3, and 55 are arranged to form the rectangle shown below. A curve is drawn by inscribing a quarter circle in each square and joining the quarter circles in order, from shortest to longest. What is the length of the curve?
4π4\pi
6π6\pi
132π\dfrac{13}{2}\pi
8π8\pi
13π13\pi
Answer: B
Concepts:arccircumference
Small hint:
Each arc is one quarter of a circle
Big hint:
Add the radii 1+1+2+3+51+1+2+3+5, then multiply by π2\frac{\pi}{2}
Video solution:
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Written solution:
Each piece of the curve is a quarter circle. The radii are 1,1,2,3,51,1,2,3,5, so the total length is 14⋅2π(1+1+2+3+5)\frac14\cdot2\pi(1+1+2+3+5) =π2⋅12=\frac{\pi}{2}\cdot12 =6π=6\pi.
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