AMC 8 2018 Problem 4
AMC8 2018 年第 4 题
面积与周长（综合）★★☆☆☆
The twelve-sided figure shown has been drawn on graph paper. What is the area of the figure in ?
如下图所示的十二边形画在 1cmｘ1cm 的画纸上。那么这个十二边形的面积是多少平方厘米？
- A.12
- B.12.5
- C.13
- D.13.5
- E.14
正确答案 · Correct Answer
C
解析 · Solution
Solution 1
We count unit squares in the middle, and 8 small triangles, which gives 4 rectangles each with an area of 1. Thus, the answer is 9+4=13.
We can see here that there are 9 total squares in the middle. We also see that the triangles that make the corners of the shape have an area half the squares' area. Then, we can easily find that each corner has an area of one square and there are 4 corners so we add that to the original 9 squares to get 9+4=13. That is how I did it.
We can apply Pick's Theorem here. There are 8 lattice points, and 12 lattice points on the boundary. Then,
Use the Shoelace Theorem and get 13.
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