Need help with solving these 2 geometry questions.

Question

1) Suppose you have a map with a scale of 1 cm = 20 km. You trace a country on the map onto a sheet of card stock, cut out the tracing, and weigh it. The tracing of the country weighs 6 grams. You find that a 30 cm by 50 cm piece of the same card stock weighs 15 grams.

What is the area of the country tracing on the card in square cm?

What is the area of the actual country in square km?

Answer 1

The 30x50 cm piece of stock has area 1500 cm². For the unknown area, use a proportion because mass should vary directly with area (for the same thickness): x / 1500 = 6 g / 15 g = 0.40, x = 600 cm² area of the tracing.

Note that in converting to km², the conversion factor must be squared: 600 cm² • (20 km /1 cm)² = 240,000 km² for the estimated area of the country.