Area and Perimeter - Counting Squares on a Grid

Perimeter is the total length of the boundary or the outer edge of a closed figure. On a square grid, you calculate it by counting the number of unit segments along the outside of the shape. Imagine walking along the black lines that outline the figure and counting each step from one grid corner to the next.

Area is the amount of surface or space covered by a closed figure. When using a grid, area is measured by counting the total number of unit squares enclosed within the shape. Visually, this is like counting how many small tiles of equal size are needed to perfectly cover the inside of the drawing.

A Unit Square is a square where each side measures $1$ unit (like $1\text{ cm}$ or $1\text{ unit}$). On a standard grid, one small box represents $1\text{ square unit}$, written as $1\text{ unit}^2$.

To find the area of regular shapes like rectangles on a grid, you can count the number of rows and the number of columns. For example, a rectangle covering $3$ rows and $4$ columns contains $3 \times 4 = 12$ unit squares.

When dealing with irregular shapes or triangles on a grid, some squares might only be partially filled. If exactly half of a square is shaded, we count it as $\frac{1}{2}$ or $0.5$ square units. Two such half-filled squares combine to make $1$ full unit square.

For complex or curved shapes on a grid, use the rule of thumb: count a square as $1$ full unit if more than half of it is covered, and ignore it (count as $0$) if less than half is covered. This provides a close estimate of the total area.

Perimeter and Area are different measurements: Perimeter measures the 'fence' around the shape (linear units like $\text{cm}$), while Area measures the 'carpet' inside the shape (square units like $\text{cm}^2$).