1978 AMC 12 Problem 7

Attempt Problem 7 of the 1978 AMC 12 below, then check your answer against the professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 1978 AMC 12 solutions, or check the answer key.

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

7.

Opposite sides of a regular hexagon are 1212 inches apart. The length of each side, in inches, is
7.57.5
626\sqrt2
525\sqrt2
923\frac92\sqrt3
434\sqrt3
Answer: E
Concepts:regular polygonspecial right triangle
Small hint:
The distance between opposite sides is twice the apothem
Big hint:
A regular hexagon of side ss has apothem 32s\frac{\sqrt3}{2}s
Solution:
The distance between opposite sides is twice the apothem, hence s3.s\sqrt3. Therefore s3=12,s\sqrt3=12, so s=123=43.s=\frac{12}{\sqrt3}=4\sqrt3.
Therefore, the correct answer is E.
LIVE by Po-Shen Loh
Programs

LIVE Classes

Self-Paced Classes

Stars

Scholarship

About Us

Who Is Po-Shen Loh?

Email Contact

Newsletter

Jobs

Become a Star

For a more Thought Full world.

© 2026 Expii, Inc.