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.
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
Of course! I'd be happy to help you solve this question step by step.
To find the actual dimensions of the rectangle, we need to use the scale of the map. The scale of 1:1000 means that 1 unit on the map represents 1000 units in actual distance. In this case, 1cm on the map represents 1000cm in actual distance.
1. Find the actual dimensions of the rectangle:
- The length of the rectangle on the map is 4cm. By applying the scale, the actual length would be 4cm x 1000 = 4000cm.
- The width of the rectangle on the map is 3cm. By applying the scale, the actual width would be 3cm x 1000 = 3000cm.
So, the actual dimensions of the rectangle are 4000cm by 3000cm.
2. Find the area on the map in square centimeters (cm²):
- To find the area on the map, we need to multiply the length and width shown on the map.
- The area on the map is 4cm x 3cm = 12cm².
3. Find the actual area in square meters (m²):
- To convert the area from cm² to m², we need to divide it by 10,000, as 1m = 100cm and 1m² = 10,000cm².
- The actual area is 12cm² ÷ 10,000 = 0.0012m².
So, the area on the map is 12cm², and the actual area is 0.0012m².
I hope this explanation helps! Let me know if you have any further questions.