If one small square in the grid is of area 4 sq. units, what is the perimeter of the rectangle drawn on the grid?

Correct Option: 24 units

To find the perimeter of the rectangle drawn on the grid, let us follow these step-by-step calculations:

Step 1: Determine the side length of one small square.
We are given that the area of one small square on the grid is $4\text{sq. units}$.
Since the area of a square is given by ${\text{side}}^2$, we can find the length of each side ($s$):

$s^2=4$

$s=\sqrt{4}=2\text{units}$

Step 2: Determine the dimensions of the rectangle from the image.
Looking at the grid image, the bold rectangle spans:

• Length ($l$) = $4$ grid units (it spans across 4 small squares horizontally)
• Width ($w$) = $2$ grid units (it spans across 2 small squares vertically)

Converting grid units to actual length units:

$\text{Length}\left(l\right)=4\times 2\text{units}=8\text{units}$

$\text{Width}\left(w\right)=2\times 2\text{units}=4\text{units}$

Step 3: Calculate the perimeter of the rectangle.
The perimeter ($P$) of a rectangle is calculated using the formula:

$P=2\times (\text{Length}+\text{Width})$

$P=2\times (8+4)$

$P=2\times 12=24\text{units}$

Thus, the perimeter of the rectangle drawn on the grid is 24 units.