1994 AMC 12 Problem 8

Attempt Problem 8 of the 1994 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 1994 AMC 12 solutions, or check the answer key.

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

In the polygon shown, each side is perpendicular to its adjacent sides, and all

28

of the sides are congruent. The perimeter of the polygon is

56.

The area of the region bounded by the polygon is

84

96

100

112

196

Each side has length

\frac{56}{28}

In units of one side length, split the shape into horizontal strips of widths

1,3,5,7,5,3,1

Each side has length

2.

Measured in side-length units, the seven horizontal strips have widths

1,3,5,7,5,3,1,

totaling

25

unit squares. Each such square has area

2^2=4,

so the polygon’s area is

25\cdot4=100.

Thus the correct answer is C.

Problem 8 in other years