AMC 8 2022 Problem 1
AMC8 2022 年第 1 题
面积与周长（综合）★☆☆☆☆
The Math Team designed a logo shaped like a multiplication symbol, shown below on a grid of 1-inch squares. What is the area of the logo in square inches?
在由边长为 1 英寸的正方形组成的方格纸上，数学小组设计了一个类似乘法符号的标志，如下图所示。问该标志的面积是多少平方英寸？
- A.10
- B.12
- C.13
- D.14
- E.15
正确答案 · Correct Answer
A
解析 · Solution
Solution 1
There are 5 lattice points in the interior of the logo and 12 lattice points on the boundary of the logo. Because of Pick's Theorem, the area of the logo is .
Notice that the area of the figure is equal to the area of the 4×4 square subtracted by the 12 triangles that are half the area of each square, which is 1. The total area of the triangles not in the figure is , so the answer is 16-6 = 10.
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