Question

图中的十二边形画在 $1 \text{ cm}\times 1 \text{ cm}$ 的方格纸上。该图形的面积是多少 $\text{cm}^2$ ？

The twelve-sided figure shown has been drawn on $1 \text{ cm}\times 1 \text{ cm}$ graph paper. What is the area of the figure in $\text{cm}^2?$

$12$

$12.5$

$13$

$13.5$

$14$

答案：C

知识点：面积分割三角形面积

难度评级：770

视频讲解：

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文字解答：

如图所示，可以把图形分解：

现在可以看出，中间是一个 $3 \times 3$ 正方形，周围有 $4$ 个较小的阴影三角形。

正方形面积为 $3 \cdot 3 = 9$ 。每个小三角形的底为 $2$ ，高为 $1$ ，所以面积是这样的三角形有 $4$ 个，所以它们的总面积为 $1\cdot 4 = 4$ 。 $\dfrac{bh}{2} = \dfrac{2\cdot 1}{2} =1 .$

因此总面积是 $9+4 = 13$ 。

所以正确答案是 C。

To solve for the area of the figure, we separate the compound shape into parts that are easier to work with, as such:

As is now clear, there is the center $3 \times 3$ square, with $4$ smaller shaded triangles surrounding it.

The area of the square is $3 \cdot 3 = 9.$ The other triangles each have a base of $2$ and a height of $1,$ so their area is equal to $\dfrac{bh}{2} = \dfrac{2\cdot 1}{2} =1 .$ There are $4$ of these triangles, so their total area is $1\cdot 4 = 4.$

Therefore, the total area is $9+4 = 13.$

Thus, the correct answer is C.

2018 AMC 8 第 4 题

答案：C

难度评级：770

视频讲解：

文字解答：

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