# building is 50cm long 38cm wide 225cm tall on the model 1 centimeter represents 2.5 meters.what is the sruface area including ceiling and floor

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The measurements of the model building:

50 cm long

38 cm wide

225 cm tall.

1 cm represent 2.5 meter

1 m = 100 cm

Then 1 cm represents 250 cm.

Then the actual building is 250 times the model building;

Then the measurements of the actual building is:

50*250 = 12500 cm = 125 m long

38*250 = 9500 cm = 95 m wide

225*250 = 56250 cm = 562.5 m tall

Now the surface are for the building= surface area for 2 base + surface area for 4 sides.

The area of the base (Ab)= 125* 95 = 11875 m^2

The area of the side (As1) = 125* 562.5 = 70312.5 m^2

The area of the side (As2) = 95* 562.5 = 53437.5 m^2

Then the total surface area= 2(Ab)+2(As1)+2(As2)

= 2(11875) +2(70312.5)+ 2(53437.5)

= 23750+140625 +106875

=271,250 m^2

length=0.5*2.5=1.25 m

width=0.38*2.5=0.95 m

hight=2.25*2.5=5.625 m

total surface area of the bulding

**2[ (l*b)+(b*h)+(l*h) ]**

**2[ (1.25*0.95)+(0.95*5.625)+(1.25*5.625) ]**

**2[ (1.1875)+(5.34375)+(7.03125) ]**

**2[ 13.5625 ]**

**27.125 m^2**

**total surface are of bulding with celling and floor is 27.125 m^2.**

1cm of model = 2.5m actual.

Therefore, actual length (l), width (w) and height (h) of the building are 50*2.5 m = 125m, 38*2.5 = 95m and 225*2.5 = 562.5 meter respepectively.

The building has 6 surfaces floor and roof whose area is lw+lw =2lw. And 4 walls whose area is lh+wh+lh+wh = 2(l+w)h.

So the floor area and roof area =2l*w = 23750 m^2

Area of 4 walls = 2(l+w)h = 2(125+95)*562.5 = 247500m^2

Therefore the surface area of the building = (23750+247500)m^2 = 271250 m^2