A house plan shows a scale of 1:25. If the rectangular lounge room of the house is to measure 4 metres by 6 metres, what will the area of the lounge room be on the plan?
The model had measurement of
4/25 m by 6/25m
= .16 m by .24 m
= 16 cm by 24 cm
area = (16)(24) cm^2
= 384 cm^2
or
area of actual room
= 400 cm by 600 cm
area = 240000 cm^2
but areas are proportional to the square of the sides, so divide by 25^2 or 625
to get 384 cm^2
To determine the area of the lounge room on the plan, we need to use the given scale of 1:25.
The scale tells us that every measurement on the plan represents 25 times its actual size.
First, we need to calculate the dimension of the lounge room on the plan. Since the length is 4 meters and the scale is 1:25, we divide the actual length by the scale:
4 meters / 25 = 0.16 meters
Similarly, we calculate the width:
6 meters / 25 = 0.24 meters
Now that we have the dimensions on the plan, we can calculate the area.
Area = Length x Width
Area = 0.16 meters x 0.24 meters
Area = 0.0384 square meters
Therefore, the area of the lounge room on the plan is 0.0384 square meters.