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Chapter 1: Problem 38

Find the perimeter and area of each figure. a square with length 18 centimeters

Short Answer

Expert verified
The perimeter is 72 cm and the area is 324 cm虏.

Step by step solution

01

Understand the Problem

We need to find both the perimeter and the area of a square with a side length of 18 centimeters. Recall that a square has four equal sides.
02

Calculate the Perimeter

The perimeter of a square is calculated by adding the lengths of all its sides. Since all sides are equal, you can multiply one side by 4. So the formula is: \[ P = 4 \times \, \text{side} \] Substituting 18 for the side length: \[ P = 4 \times 18 = 72 \, \text{cm} \]
03

Calculate the Area

The area of a square is found by squaring the length of one of its sides. The formula is: \[ A = \text{side}^2 \] Substituting 18 for the side length: \[ A = 18^2 = 324 \, \text{cm}^2 \]

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Key Concepts

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

Perimeter
The perimeter of a geometric shape is the total distance around the outer edge. For a square, which has four identical sides:
perimeter is the result of adding all four sides together. Rather than adding four separate numbers, you can multiply the length of one side by four.
This gives us the formula:
  • \( P = 4 \times \text{side} \)
In our example, where each side is 18 centimeters, the perimeter becomes:
  • \( P = 4 \times 18 = 72 \text{ cm} \)
It's important to recognize that understanding perimeter is crucial not only in math problems but also in real life. For instance, if you were planning a fence around a square garden, knowing how to calculate the perimeter tells you the total length of the fence you would need.
Area Calculation
The area of a shape in geometry refers to the amount of space it occupies on a flat plane. For squares, the area is found by squaring the side length. This process reflects the idea that you are creating a grid of squares within the larger shape.
To find the area, use the formula:
  • \( A = \text{side}^2 \)
For our square with a side of 18 centimeters, the area calculation is:
  • \( A = 18^2 = 324 \text{ cm}^2 \)
Area is different from perimeter because it reflects coverage rather than boundary. Consider if you were laying down flooring tiles in a square room; you would need to know the area to purchase the right amount of tiles.
Square Properties
Squares are special types of rectangles. They stand out in geometry due to their unique properties:
  • All sides are equal in length.
  • All internal angles are right angles (each measuring 90掳).
These properties mean that a square is both a rectangle (because it has right angles and opposite sides that are equal) and a rhombus (because all sides are the same length).
Due to these properties, calculations involving squares, like finding perimeter and area, are straightforward. They offer a great starting point for exploring more complex shapes in geometry. When designing anything square in shape, understanding these properties ensures both aesthetic balance and mathematical accuracy.

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