Question

Tamara 的花园里有三排花坛，每排有两个 $6$ 英尺乘 $2$ 英尺的花坛。花坛之间以及花坛外侧都有 $1$ 英尺宽的小路，如图所示。所有小路的总面积是多少平方英尺？

Tamara has three rows of two $6$ -feet by $2$ -feet flower beds in her garden. The beds are separated and also surrounded by $1$ -foot-wide walkways, as shown on the diagram. What is the total area of the walkways, in square feet?

$72$

$78$

$90$

$120$

$150$

答案：B

知识点：面积分割矩形

难度评级：960

解答：

花园总宽为总高为因此外部大矩形面积为 $15 \cdot 10 = 150$ 。所有花坛面积为用总面积减去花坛面积，得到小路面积 $150 - 72 = 78$ 。 $2 \cdot 6 + 3 \cdot 1 = 15.$ $3 \cdot 2 + 4 \cdot 1 = 10.$ $6 \cdot 2 \cdot 6 = 72.$

所以正确答案是 B。

We can see that the width of the garden is $2 \cdot 6 + 3 \cdot 1 = 15.$ We can also see that the height is $3 \cdot 2 + 4 \cdot 1 = 10.$ The total area of the garden is therefore $15 \cdot 10 = 150.$ The area of all the flower beds is $6 \cdot 2 \cdot 6 = 72.$ Subtracting this from the area of the garden yields $150 - 72 = 78,$ which is the area of the walkways.

Thus, B is the correct answer.

2017 AMC 10A 第 3 题

答案：B

难度评级：960

解答：

其他年份的第 3 题