If you are a geography student, you may have encountered the challenge of calculating the area of a region on a topographical map. A topographical map is a type of map that shows the physical features of the land, such as hills, valleys, rivers, lakes, etc. The map also uses contour lines to indicate the elevation or height of the land at different points.

Calculating the area on a topographical map is not as simple as measuring the length and width of a rectangle. You have to take into account the shape and size of the region, as well as the scale and projection of the map. In this article, we will show you how to calculate the area on a topographical map using a simple formula and some examples.

The formula for calculating the area on a topographical map is:

Area = (Scale Factor) x (Area on Map)

The scale factor is a number that represents how much the map has been reduced or enlarged from the actual size of the land. For example, if the scale of the map is 1:50,000, it means that one centimeter on the map equals 50,000 centimeters or 500 meters on the land. The scale factor is calculated by dividing one by the scale ratio. For example, if the scale is 1:50,000, the scale factor is 1/50,000 or 0.00002.

The area on map is the area of the region on the map measured in square centimeters. You can use different methods to measure the area on map depending on the shape of the region. For example, you can use a ruler and a calculator to measure the area of a rectangle or a triangle. You can also use a grid paper or a planimeter to measure irregular shapes.

Let’s look at some examples of calculating area on topographical map using the formula.

Suppose you want to calculate the area of a rectangular region on a topographical map with a scale of 1:25,000. The length and width of the rectangle are 8 cm and 6 cm respectively. What is the area of the region on the land?

To solve this problem, we need to apply the formula:

Area = (Scale Factor) x (Area on Map)

The scale factor is 1/25,000 or 0.00004.

The area on map is 8 cm x 6 cm or 48 cm.

Therefore, the area of the region on the land is:

Area = (0.00004) x (48)

Area = 0.00192 km

Suppose you want to calculate the area of a triangular region on a topographical map with a scale of 1:100,000. The base and height of the triangle are 10 cm and 12 cm respectively. What is the area of the region on the land?

To solve this problem, we need to apply the formula:

Area = (Scale Factor) x (Area on Map)

The scale factor is 1/100,000 or 0.00001.

The area on map is (1/2) x (10 cm) x (12 cm) or 60 cm.

Therefore, the area of the region on the land is:

Area = (0.00001) x (60)

Area = 0.0006 km