Approximately what is the area of the county?

Question

You have a map on which 1 inch represents 2.5 miles. You cover a county on the map with a 1/8 inch thick layer of molding dough. Then you re-form this piece of modeling dough into a 1/8 inch thick rectangle. The rectangle is 1 3/4 inches by 2 1/4 inches. 

Answer 1

By reforming the area of the country into a rectangle, you have a rectangle with approximately the same area as the country itself.  If you calculate the area of the rectangle, then you know the area of the country.

 

Remember, the area of a rectangle is base time height.  However, if you simply multiply the 1 3/4 by the 2 1/4, you will know the area in the scaled measurements, not in real measurements.

 

First convert the scaled measurements of the sides to their real counterparts.

 

1 3/4 x 2.5 = 4 3/8 miles

2 1/4 x 2.5 = 5 5/8 miles

 

Therefore, the area of the country is:

4 3/8 x 5 5/8 = 24 39/64 square miles ≈ 24.6 mi².