# In a map of scale 1 : 500 , the length and breath of a rectangular field are 2 cm and 3cm respectively. Find the actual area of this field. A. 30 m^2 B. 150 m^2 C. 1 500 m^2 D. 3 000 m^2 E. 15 000 m^2

In the map all dimensions are scaled down by a ratio 1: 500. Every unit of length used on the map corresponds to 500 units of length in the real world.

If an area on the map has dimensions 2 cm * 3 cm, the actual area in the real world is 2*500*3*500 cm^2 = 1500000 cm^2. One cm^2 = `1/10000` m^2, 1500000 cm^2 = `1500000/100000` = 150 m^2

The actual area of a rectangular block with dimensions 2 cm* 3 cm on the map is 150 m^2.

The correct answer is option B

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scale 1: 500 means that `500m^2` in the actual ground is represented by `1cm^2` on the map. Or in other words `500m^2` is shown in `1cmxx1cm` square on map.

Area of map `= 2xx3 = 6cm^2`

Actual area `= 6xx500m^2 = 3000m^2`

So the area of actual field is `3000m^2` and the correct answer is at option D.

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