Sure, let's solve this problem step-by-step.
First, we need to understand the scale notation. The scale of 1:100 means that 1 unit of length on the map represents 100 units of length in the actual field.
1. Determine the actual width of the field:
- The width of the field on the map is given as 8 cm.
- Since the scale is 1:100, the actual width of the field can be calculated by multiplying the map width by the scale factor.
[tex]\[
\text{Actual width} = 8 \text{ cm} \times 100 = 800 \text{ cm}
\][/tex]
2. Determine the actual area of the field:
- The area of the field on the map is given as [tex]\( 58 \, \text{cm}^2 \)[/tex].
- The scale factor for area is the square of the linear scale factor. Given the scale is 1:100, the scale factor for area will be [tex]\( 100^2 \)[/tex] or 10,000.
[tex]\[
\text{Actual area} = 58 \text{ cm}^2 \times 10,000 = 580,000 \text{ cm}^2
\][/tex]
3. Convert the actual area to square meters:
- To convert from square centimeters to square meters, we use the conversion factor [tex]\( 1 \text{ m}^2 = 10,000 \text{ cm}^2 \)[/tex].
[tex]\[
\text{Actual area in } m^2 = \frac{580,000 \text{ cm}^2}{10,000 \text{ cm}^2/\text{m}^2} = 58 \text{ m}^2
\][/tex]
So, the area of the actual field is [tex]\( 58 \, \text{m}^2 \)[/tex].
