Introduction
Think about a city park in your neighborhood. Have you noticed how the space is divided into different sections? You might see playgrounds, walking paths, sports fields, and garden areas. Each section likely has a different shape and size based on its purpose. This raises interesting questions: How do city planners decide how to divide these spaces? When they need to create equal sections for different activities, what methods do they use?
Consider a landscape architect planning a new community garden. How do they calculate how much soil, mulch, or irrigation equipment is needed? Isn't it fascinating how the size and shape of the space directly influences these calculations?
The development of geometry has deep roots in urban planning and architecture. Ancient civilizations, like the Greeks with their agoras (public squares) and the Romans with their carefully planned cities, used geometric principles to organize public spaces. Even today, we see buildings and spaces in various geometric shapes - some are perfect rectangles like office buildings, others are circular like sports arenas, and some have irregular shapes that follow natural land contours.
To understand these spaces better, we need to learn how to measure and calculate areas of different shapes. In this chapter, we'll explore how to find the areas of basic geometric figures like squares, rectangles, and triangles using mathematical formulas. More importantly, we'll understand why these formulas work and how they were developed, giving us the tools to work with both regular and irregular spaces in our modern world.
This approach maintains the core geometric concepts while making them relevant to contemporary urban life, rather than using agricultural examples.