I don’t understand the question or concept at all please help.

On a floor plan drawn at a scale of 1:100, the area of a rectangular room is 30cm^2. What is the actual area of the room?

Answer: 30 m^2

1:100 mean:

1cm of a plan drawn represents 100 cm

100 cm = 1 m

1cm of a plan drawn represents 1m

1 cm x 1 cm = 1cm²

If 1cm of a plan drawn represents 1m then 1cm² of a plan drawn represents 1m²

30 cm² represents 30 m²

To understand the question and concept, let's break it down step by step.

1. Scale: In this case, the floor plan is drawn at a scale of 1:100. A scale represents the relationship between measurements on the drawing and the actual measurements. For example, if the scale is 1:100, it means that one unit on the drawing represents 100 units in actual size.

2. Area of the room: The question provides the area of the room on the floor plan, which is 30 cm^2. Keep in mind that this measurement is based on the scale of 1:100.

To find the actual area of the room, we need to convert the floor plan area back to its actual size. Here's how to do it:

Step 1: Determine the conversion factor. The scale of 1:100 means that 1 cm on the drawing represents 100 cm in reality. To convert from the drawing scale to the actual scale, divide the drawing measurement by the scale. In this case, 30 cm^2 / 100 = 0.3 cm^2.

Step 2: Convert from centimeters (cm) to meters (m). Since we need the area in square meters (m^2), we need to convert cm^2 to m^2. To do this, divide the converted area (0.3 cm^2) by 10,000. Why 10,000? Because there are 10,000 square centimeters in a square meter. So, 0.3 cm^2 / 10,000 = 0.00003 m^2.

Therefore, the actual area of the room is 0.00003 square meters or simply 30 m^2.