LAB 3. WORKED EXAMPLES

1. How many kilometers would be represented by 5 cm at a scale of 1:20,000?

5 cm represents 5 x 20,000 cm = 100,000 cm = 100,000/100,000 = 1 km.

(remember that there are 100,000 cm in 1 km).

2. Using the representative fraction, calculate the straight-line distance in a) miles, b) kilometers, from point A to point B:

A

B

a) RF = 1:24,000

Map distance A-B = 4.3 inches

Actual distance = 103,200 inches = 103,200/63360 = 1.63 miles (rounded to 2 decimal places).

(remember that there are 63360 inches in one mile).

b) RF = 1:24,000

Map distance A-B = 11 cm

Actual distance = 264,000 cm = 264,000/100,000 = 2.64 km (rounded to 2 decimal places).

3. At a scale of 1:50,000, a) how much area in square miles would be represented by a rectangle measuring 1 inch by 2 inches? b) how much area in square kilometers would be represented by a rectangle measuring 3 by 5 cm?

a) 1 inch represents 1 x 50,000 inches = 50,000 inches = 50,000/63360 = 0.789 miles.

2 inches represents 2 x 50,000 inches = 100,000 inches = 100,000/63360 = 1.58 miles.

0.789 miles x 1.58 miles = 1.23 miles²

b) b) 3 cm represents 3 x 50,000 cm = 150,000 cm = 150,000/100,000 = 1.5 km.

5 cm represents 5 x 50,000 cm = 250,000 cm = 250,000/100,000 = 2.5 km.

1.5 km x 2.5 km = 3.75 km²