the plan of a shopping complex is drawn to a scale of 1:400. A supermarket on the plan occupies an area of 0.25m square, calculate its actual area in hectares

The scale of 1:400 states a linear relation and we know that the areas of similar figures is proprotional to the square of the corresponding sides

so ...
actual area/.25 = 400^2/1^2
actual area = 40000 m^2
since 1 hectare = 10,000 m^2
the actual area = 40000/10000 = 4 hectares

or

.25 m^2 would give a side of .5 m on the scale drawing
which would be .5(400) or 200 m in real life
so the area of the complex in real life is
200 m by 200 m = 40,000 m^2 , etc same as above

To calculate the actual area of the supermarket in hectares, we need to convert the given area from square meters to hectares.

Step 1: Convert the area from square meters to square kilometers.
1 hectare = 10,000 square meters (by definition)
So, 0.25 square meters = 0.25/10,000 square kilometers

Step 2: Convert the area from square kilometers to hectares.
1 square kilometer = 100 hectares (by definition)
Therefore, 0.25/10,000 square kilometer = (0.25/10,000) * 100 hectares

Now let's calculate the actual area of the supermarket in hectares:

(0.25/10,000) * 100 hectares = 0.0025 hectares

Therefore, the actual area of the supermarket is 0.0025 hectares.