The figure on the side shows a grid formed by squares with a side of $1 \mathrm{~cm}$. What is the ratio between the shaded area and the unshaded area?
(a) $\frac{1}{4}$
(b) $\frac{1}{5}$
(c) $\frac{1}{6}$
(d) $\frac{2}{5}$
(e) $\frac{2}{7}$

![](https://cdn.mathpix.com/cropped/2024_05_01_280b19a87fa67143351eg-006.jpg?height=262&width=271&top_left_y=2396&top_left_x=1555)
The correct option is (a).

The grid is a square with a side length of $5 \mathrm{~cm}$, so its area is equal to $25 \mathrm{~cm}^{2}$. The shaded part of the grid is formed by four triangles, two of which have a base of $1 \mathrm{~cm}$ and a height of $2 \mathrm{~cm}$, and the other two have a base of $1 \mathrm{~cm}$ and a height of $3 \mathrm{~cm}$. Therefore, the shaded area is equal to $2 \times \frac{1}{2}(1 \times 2)+2 \times \frac{1}{2}(1 \times 3)=5 \mathrm{~cm}^{2}$ and the unshaded area is equal to $25-5=20 \mathrm{~cm}^{2}$. Thus, the required ratio is $5 / 20=1 / 4$.