Step 1: Convert the linear scale into an area multiplier first.
A quick way to handle these problems without redoing unit algebra each time is to square the metres per centimetre figure directly. Here, 1 cm on the plan stands for 10 m on the ground, so every 1 cm\(^2\) patch of paper stands for $10 \times 10 = 100$ m\(^2\) of real ground.
Step 2: Scale the given plan area by that multiplier.
The plan shows an area of 10 cm\(^2\). Since each of those square centimetres is worth 100 m\(^2\) on the ground, the total ground area is simply
\[ 10 \times 100 = 1000 \text{ m}^2 \]
Step 3: Sanity check with an alternative unit path.
We can double check by converting everything into centimetres first: 10 m = 1000 cm, so the linear scale is 1 cm : 1000 cm, and the area scale is $1 : 1000^2 = 1 : 1{,}000{,}000$ (cm\(^2\) to cm\(^2\)). Multiplying $10 \text{ cm}^2 \times 1{,}000{,}000 = 10{,}000{,}000 \text{ cm}^2$, and converting back to m\(^2\) by dividing by $10{,}000$ (since 1 m\(^2\) = 10,000 cm\(^2\)) gives 1000 m\(^2\) again, confirming the answer.
\[ \boxed{1000 \text{ m}^2} \]