SOLUTION: 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

Question 1098496: 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
Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
On the floorplan the building may be a rectangle with a certain length and width.
If it is so, and those length and width measurements, in m, are represented by and respectively,
.
The actual building length and width measurements, in m, are
and ,
so its surface area in can be calculated as
.
I was taught in elementary school, than an are is ,
and that the prefix "hecto" means .
so (about the surface area of a city block),
and is

But what if the building shape is not a rectangle?
Any 2-D or 3-D shape can be approximated by an arrangement of squares or cubes,
so for any shape that is scaled up or down to get a similar shape
by multiplying all corresponding lengths times a factor ,
all corresponding surface areas are multiplied times ,
and all corresponding volumes are multiplied times .

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