Fields and Fences - Counting Squares to find Area

Area is the measure of the total surface or space covered inside a closed flat shape. Visually, if you imagine a field of grass, the area is the entire green space where you can walk, while the fence is just the boundary around it.

To measure area, we use 'Unit Squares.' A unit square is a square where every side is exactly $1$ unit long (like $1\text{ cm}$ or $1\text{ meter}$). On grid paper, we calculate area by counting how many of these small square boxes fit inside a shape.

For simple shapes on a grid, we count every complete square box that is fully inside the boundary. If a rectangle encloses $12$ full boxes, its area is $12\text{ square units}$.

The Half-Square Rule: If a shape covers exactly half of a grid square, we count it as $\frac{1}{2}$. Visually, two such half-squares (which often look like triangles) can be joined together to make $1$ full square unit.

For irregular shapes like leaves or handprints, we use the 'More than Half' rule: if a square is more than half-filled by the shape, we count it as $1$ full square. If it is less than half-filled, we count it as $0$.

Area is always expressed in square units. For small shapes drawn on paper, we use square centimeters ($\text{sq. cm}$); for large fields or gardens, we use square meters ($\text{sq. m}$).

A rectangle's area can be visualized as an array of rows and columns. If a rectangle has $3$ rows of squares and $5$ columns, you can find the total area by multiplying the two numbers: $3 \times 5 = 15$ squares.

Even if two shapes have the same perimeter (the same length of fence), they can have different areas. A long, thin rectangle might have a smaller area than a square made from the same length of string.