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

Hello Sasha,

One way to answer this question is to write the corresponding proportion. That is, the area of the similar card stock is to the weight of the similar card stock as the area of the tracing of the country on the map is to the weight of the cut out tracing of the country.

(Area of (30 cm x 50 cm) card stock) ÷ (Weight of the card stock) = (Area of country in cm²) ÷ (Weight of cut out tracing)

Area of 30 cm x 50 cm = 1500 cm²

Weight of card stock = 15 g

Area of country in cm² = x

Weight of cut out tracing = 6g

1500 ÷ 15 = x ÷ 6, Multiply both sides by 6

x = (1500 ÷ 15)*6

x = 600

Hence the area of the country tracing on the card is 600 cm² .

Given the scale 1 cm = 20 km, it follows that (1 cm)² = (20 km)², that is, 1 cm² = 400 km²

So the area of the actual country in km² is 600 cm² times 400 km² = 240000 km²