A rectangular field measuring 560 m by 800 m is to be represented on a scale drawing using the scale 1:20000. What is the area of the scale drawing in square centimeters?
To find the area of the scale drawing in square centimeters, we need to determine the dimensions of the scale drawing and then calculate its area.
First, let's calculate the dimensions of the scale drawing:
Given that the scale is 1:20000, it means that 1 unit on the scale drawing represents 20000 units in reality.
To find the length dimension of the scale drawing, we divide the actual length of the field (560 m) by the scale factor:
Length of scale drawing = (Actual length / Scale factor) = 560 m / 20000 = 0.028 m
Similarly, to find the width dimension of the scale drawing, we divide the actual width of the field (800 m) by the scale factor:
Width of scale drawing = (Actual width / Scale factor) = 800 m / 20000 = 0.04 m
Now that we have the dimensions of the scale drawing, we can calculate its area:
Area of scale drawing = Length × Width = 0.028 m × 0.04 m = 0.00112 square meters
Since we need the area in square centimeters, we can convert square meters to square centimeters:
1 square meter = 10000 square centimeters
0.00112 square meters × 10000 = 11.2 square centimeters
Therefore, the area of the scale drawing is 11.2 square centimeters.