How do you calculate the real area from a 1:100 scale drawing?

To calculate the real area from a 1:100 scale drawing, multiply the drawing area by 10,000.

When working with scale drawings, it's important to understand that the scale factor applies to both the lengths and the areas. A 1:100 scale means that 1 unit on the drawing represents 100 units in real life. However, when dealing with areas, the scale factor is squared. This is because area is a two-dimensional measurement (length × width).

For example, if you have a rectangle on a 1:100 scale drawing that measures 2 cm by 3 cm, you first calculate the area on the drawing: 2 cm × 3 cm = 6 cm². To find the real area, you need to multiply this drawing area by the square of the scale factor. Since the scale factor is 100, you square it to get 10,000. Therefore, the real area is 6 cm² × 10,000 = 60,000 cm².

To convert this into more familiar units, you might want to change square centimetres to square metres. There are 10,000 cm² in 1 m², so 60,000 cm² is equal to 6 m². Thus, the real area of the rectangle is 6 square metres.

Remember, the key step is squaring the scale factor (100² = 10,000) and then multiplying it by the area on the drawing. This method ensures you accurately convert the scaled area to the real-world area.