Asked by alain
Would you guys mind help me to solve this question? : The scale of a map is 1:1000. What are the actual dimensions of a rectangle which appears as 4cm by 3cm on the map? What is the area on the map in cm squared?what is the actual area in meter squared? I would like to see the way it is done not just answers.thank you.
Answers
Answered by
Steve
the real world has dimensions 1000 times as large as the map, so
4cm -> 4000cm = 40m
3cm -> 3000cm = 30m
the map area is 3cm * 4cm = 12 cm^2
the actual area is
40m * 30m = 1200 m^2
or, you can use the scale factor to figure the real area. Since area is length * width, the scale factor gets used twice, so the area's scale factor is 1000^2 = 1,000,000
3*4*1000000 = 12000000 cm^2
Divide that by 100^2 (cm^2/m^2) and you get
1200 m^2
4cm -> 4000cm = 40m
3cm -> 3000cm = 30m
the map area is 3cm * 4cm = 12 cm^2
the actual area is
40m * 30m = 1200 m^2
or, you can use the scale factor to figure the real area. Since area is length * width, the scale factor gets used twice, so the area's scale factor is 1000^2 = 1,000,000
3*4*1000000 = 12000000 cm^2
Divide that by 100^2 (cm^2/m^2) and you get
1200 m^2