AMC8 2018

AMC8 2018 · Q4

AMC8 2018 · Q4. It mainly tests Area & perimeter, Counting in geometry (lattice points).

The twelve-sided figure shown has been drawn on 1 cm × 1 cm graph paper. What is the area of the figure in cm²?

图中所示的十二边形是在 1 cm × 1 cm 方格纸上绘制的。该图形的面积是多少平方厘米？

(A) 12 12

(B) 12.5 12.5

(D) 13.5 13.5

(E) 14 14

Answer

Correct choice: (C)

正确答案：（C）

Solution

Answer (C): In the figure below, the square RSTU has side length 3, so its area is $3^2=9$, and $\triangle REF$ has area $1$. The other three triangles are congruent to $\triangle REF$, so the total area is $9+4\cdot1=13$.

解答（C）：如图所示，正方形 RSTU 的边长为 3，因此其面积为 $3^2=9$，且三角形 $\triangle REF$ 的面积为 $1$。其余三个三角形与 $\triangle REF$ 全等，所以总面积为 $9+4\cdot1=13$。

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