To determine the actual area from a scale drawing, you need to multiply the area measured in the drawing by the square of the scale factor.

Understanding the scale factor is crucial when working with scale drawings. The scale factor represents the ratio of any length in the drawing to the corresponding actual length. For instance, a scale of $1:100$ indicates that 1 unit on the drawing corresponds to $100$ units in reality.

To compute the actual area, start by calculating the area on the scale drawing. This involves measuring the length and width of the shape depicted in the drawing and applying the appropriate area formula (for example, length × width for a rectangle).

Next, you will need to square the scale factor. If the scale is $1:100$, the scale factor is $100$. Squaring this gives you $100^2 = 10,000$. This squared scale factor accounts for the scaling of both dimensions (length and width).

Finally, to find the actual area, multiply the area obtained from the scale drawing by the squared scale factor. For example, if the area measured on the drawing is $5 \, \text{cm}^2$ and the scale is $1:100$, the calculation for the actual area would be:

This method ensures an accurate conversion from the area depicted in the scale drawing to the actual area, considering the two-dimensional nature of area measurements.