2002 AMC 8 Problem 15

Below is the professionally curated solution for Problem 15 of the 2002 AMC 8, from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2002 AMC 8 solutions, or check the answer key.

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Concepts:area lattice point

Difficulty rating: 1290

15.

Which of the following polygons has the largest area?

$\text{A}$

$\text{B}$

$\text{C}$

$\text{D}$

$\text{E}$

Solution:

The number of boxes enclosed by each polygon can be obtained by dividing the polygon into unit squares and right triangles with sidelength $1$ and adding up their values.

The unit squares count as $1$ and the triangles count as $.5.$

$A$ has a total area of $5,$ $B$ has $5,$ $C$ has $5,$ $D$ has $4.5,$ and $E$ has $5.5.$

Thus, E is the correct answer.

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