AMC8 2007

AMC8 2007 · Q23

AMC8 2007 · Q23. It mainly tests Area & perimeter.

What is the area of the shaded pinwheel shown in the 5 × 5 grid?

5×5网格中所示的阴影风车图案的面积是多少？

(A) 4 4

(B) 6 6

(D) 10 10

(E) 12 12

Answer

Correct choice: (B)

正确答案：（B）

Solution

(B) Find the area of the unshaded portion of the $5\times 5$ grid, then subtract the unshaded area from the total area of the grid. The unshaded triangle in the middle of the top of the $5\times 5$ grid has a base of $3$ and an altitude of $\frac{5}{2}$. The four unshaded triangles have a total area of $4\times \frac{1}{2}\times 3\times \frac{5}{2}=15$ square units. The four corner squares are also unshaded, so the shaded pinwheel has an area of $25-15-4=6$ square units.

（B）先求出 $5\times 5$ 方格中未阴影部分的面积，然后用方格的总面积减去未阴影面积。位于 $5\times 5$ 方格顶部中间的未阴影三角形，底为 $3$，高为 $\frac{5}{2}$。四个未阴影三角形的总面积为 $4\times \frac{1}{2}\times 3\times \frac{5}{2}=15$ 平方单位。四个角上的小正方形也未着阴影，因此阴影风车形的面积为 $25-15-4=6$ 平方单位。

Topics

GE.007 Area & perimeter