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Chapter 7: Problem 87

What is the area of a square patio that measures \(8.5 \mathrm{m}\) on each side?

Short Answer

Expert verified
The area of the square patio is \(72.25 \mathrm{m^2}\).

Step by step solution

01

Identify the length of the side of the square

Given in the question, the length of the side of the square is \(8.5 \mathrm{m}\).
02

Apply the formula for the area of a square

The formula for calculating the area of a square is \(Area\ =\ side^2\). Substitute the given side length into the formula.
03

Calculate the area

The area of the square is therefore, \(Area\ =\ 8.5m^2 = 72.25 \mathrm{m^2}\).

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Understanding a Square
A square is a simple shape in geometry. It is a four-sided figure, known as a quadrilateral. All four sides of a square are equal in length, making it unique from other quadrilaterals like rectangles or parallelograms.
Another important property of a square is its angles. Each of the four angles in a square is a right angle, measuring 90 degrees. Because of these properties, squares are everywhere in our daily lives, from tiles on a floor to shapes of coasters. Understanding squares provides a foundation for many concepts in geometry and measurement.
Understanding Measurement Units
Measurement units are critical for accurately communicating the size or extent of something. In this exercise, we're dealing with meters (\(\mathrm{m}\)). Meters are a unit of length in the metric system. They are commonly used around the world for scientific and everyday measurements.
The area of a square or any shape is often expressed using square units. This reflects the two-dimensional nature of area, such as square meters (\(\mathrm{m^2}\)). This unit helps us understand the size of a surface or region, like the surface of a patio or a garden plot.
Applying the Formula for Area
The formula for finding the area of a square is straightforward: \[Area = side^2\]Here, "side" represents the length of one side of the square.
  • The formula shows that to find the area, you multiply the length of the side by itself.
  • In our example, each side is \(8.5 \mathrm{m}\).
So, the area = \(8.5 \mathrm{m} \times 8.5 \mathrm{m} = 72.25 \mathrm{m^2}\).
This calculation explains how large the patio surface is in square meters.
The Basics of Geometry
Basic geometry helps us understand the properties of space and shapes. It covers fundamental concepts such as points, lines, angles, surfaces, and solids.
Understanding shapes like squares, rectangles, and circles is part of basic geometry. These principles are not only used in academics but also in real-world applications like architecture, engineering, and design.
  • Geometry helps us measure areas and perimeters.
  • It aids in visualizing and constructing spaces.
By getting comfortable with basic geometry, you'll find it easier to tackle problems involving measurements and spatial reasoning.

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Most popular questions from this chapter

The length of the base of a parallelogram is 16 in., and the height is 12 in. Find the area of the parallelogram.

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