Problem 51 - Prealgebra

Question

A public swimming pool measures 100 meters by 30 meters and is rectangular. What is the area of the pool in ares?

Step-by-Step Solution

Answer

The area of the pool is 30 ares.

Step 1: Understanding the Problem

We need to find the area of a rectangular swimming pool which measures 100 meters in length and 30 meters in width. After finding this area, we'll convert the result into ares.

Step 2: Calculating the Area in Square Meters

The formula to calculate the area of a rectangle is: \[ \text{Area} = \text{Length} \times \text{Width} \]Substitute the given values:\[ \text{Area} = 100 \text{ meters} \times 30 \text{ meters} = 3000 \text{ square meters} \]

Step 3: Converting the Area to Ares

1 are is equivalent to 100 square meters. So, to convert the area from square meters to ares, we divide the area by 100:\[ \text{Area in ares} = \frac{3000 \text{ square meters}}{100} = 30 \text{ ares} \]

Key Concepts

Understanding Rectangles

A rectangle is a simple yet fascinating shape in geometry. It is defined as a quadrilateral with four right angles. This means each internal angle is 90 degrees, creating a shape that has a very regular and predictable pattern. Rectangles are characterized by opposite sides being equal in length.
The longer side of a rectangle is typically called the length, while the shorter side is referred to as the width. Knowing these measurements allows us to calculate various properties of rectangles, such as perimeter and area. In practical situations, such as finding the area of a swimming pool, understanding these basic properties is essential. By multiplying the length by the width, we can determine the area, which represents the total space occupied within its boundaries.

Converting Area into Ares

Area conversion is a critical concept when measuring and understanding space, especially in different measurement systems. In this exercise, we dealt with converting the area from square meters to ares. But what is an 'are'?

• An "are" is a metric unit of area, commonly used to measure land and larger spaces like fields or parks.
• 1 are is defined as exactly 100 square meters, making it a convenient unit for converting larger areas from square meters.

Converting from square meters to ares involves a simple division. As per the original exercise, once you have the area calculated in square meters, dividing that number by 100 translates it into ares. Hence, 3000 square meters becomes 30 ares. Understanding these conversion processes helps in dealing with real-world measurements effectively.

The Geometry Behind Measure

Geometry is the branch of mathematics that focuses on properties and relations of points, lines, surfaces, and solids. When we calculate the area of a rectangle, we are applying basic principles of geometry.
In the context of geometry:

• The formula for the area is derived from multiplying two linear measurements: length and width. This gives a two-dimensional space the rectangle occupies.
• Understanding the relations between different geometric shapes and their measurements is crucial for everyday applications.

Geometry also helps us visualize and solve problems involving spatial relationships, like fitting furniture in a room or assessing how much material is needed for construction. By learning how to calculate areas, we grasp a fundamental concept of how space works in our physical world.