AMC 8 2004 Problem 14
AMC8 2004 年第 14 题
面积与周长（综合）★★★☆☆
What is the area enclosed by the geoboard quadrilateral below?
由下图中几何板上的四边形包围的面积的是多少？
- A.15
- B.
- C.
- D.27
- E.41
正确答案 · Correct Answer
C
解析 · Solution
Solution 1
Divide the shape up as above.
Let the bottom left corner be (0,0). The points would then be (4,0),(0,5),(3,4), and (10,10). Applying the Shoelace Theorem,
$\text{Area} = \frac12
$
The figure contains 21 interior points and 5 boundary points. Using Pick's Theorem, the area is
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