Identify the relationship

In a rectangle, the diagonal divides it into two right-angled triangles. We use the Pythagorean theorem where $d^2 = a^2 + b^2$.

$100^2 = 80^2 + b^2$

Calculate the missing side

Subtract the square of the known side from the square of the diagonal: $b^2 = 10000 - 6400 = 3600$. Thus, $b = \sqrt{3600}$.

$b = 60 \text{ m}$

Calculate the area

Apply the area formula for a rectangle: $\text{Area} = \text{length} \times \text{breadth}$.

$\text{Area} = 80 \times 60 = 4800 \text{ square meters}$