Question

Interpret Scientific Illustrations One hectare, shown here, is a square of land measuring 100 meters by 100 meters. How many hectares are in \(50,000 \mathrm{~m}^{2}\) of land?

Short answer

50,000 square meters is equal to 5 hectares.

Step-by-step solution

Understand a Hectare

A hectare is defined as a square with each side measuring 100 meters. Therefore, to find how much area it covers, calculate it as follows:\[ 100 ext{ meters} imes 100 ext{ meters} = 10,000 ext{ m}^2 \]So, one hectare is equal to 10,000 square meters.

Calculate the Number of Hectares

Given that we have a total area of 50,000 square meters, we need to determine how many hectares it contains. To do this, divide the total area in square meters by the number of square meters in one hectare:\[ \frac{50,000 ext{ m}^2}{10,000 ext{ m}^2/ ext{hectare}} = 5 ext{ hectares} \]Therefore, 50,000 square meters is equal to 5 hectares.

Key concepts

Area Calculation

Calculating area is an essential skill in scientific measurement. It involves finding the surface covered by a two-dimensional shape. For squares and rectangles, the area is calculated by multiplying the length of one side by the length of the other side.

In our example, a hectare represents a square that is 100 meters on each side. Therefore, its area is obtained using the formula:\[ Area = ext{length} imes ext{width} = 100 ext{ m} imes 100 ext{ m} = 10,000 ext{ m}^2 \]This simple multiplication gives us the total square meters of land covered by a hectare.

In many instances, determining area helps us understand the size of a plot of land or a field.

Conversion of Units

When performing area calculations, understanding unit conversions is crucial. Units help us to measure and compare different quantities. It is important to ensure that the units of measurement are consistent before performing mathematical operations.

For example, if we are working with hectares and square meters, we need to understand the relationship between these units:

• 1 hectare equals 10,000 square meters

Conversion requires dividing or multiplying by a conversion factor. In our example, we have 50,000 square meters and need to find out how many hectares that is. By dividing the total area (in square meters) by 10,000 square meters (1 hectare), we convert the units:\[\frac{50,000 ext{ m}^2}{10,000 ext{ m}^2/ ext{hectare}} = 5 ext{ hectares} \]

Converting units accurately ensures that comparisons and calculations are meaningful and correct.

Hectares

The hectare is a unit of area commonly used for large plots of land. It is widely used in agriculture, forestry, and land management to easily convey large land areas. A hectare simplifies land measurement through its clear size definition.

One distinct advantage of using hectares is its consistency. A hectare always measures the same amount of land ( 10,000 ext{ m}^2 ). This standard measurement makes it easier to calculate and think about large areas without converting between various systems or units.

For example, if someone is talking about a farm that covers 15 hectares, it immediately gives an intuitive sense of the land's size, especially where metric units are regularly used. Understanding and using hectares enhances our ability to communicate effectively in fields involving land and property.