Chapter 1: Problem 38
A parking lot is \(144.3 \mathrm{~m}\) long and \(47.66 \mathrm{~m}\) wide. (a) What is the perimeter of the lot? (b) What is its area?
Short Answer
Expert verified
(a) Perimeter is 383.92 m; (b) Area is 6875.538 m².
Step by step solution
01
Understanding Perimeter
The perimeter of a rectangle can be calculated using the formula: \[ P = 2(l + w) \] where \( l \) is the length and \( w \) is the width of the rectangle.
02
Calculating Perimeter
Substitute the given values into the formula for perimeter. Here, \( l = 144.3 \mathrm{~m} \) and \( w = 47.66 \mathrm{~m} \). So, \[ P = 2(144.3 + 47.66) \] Calculate the sum inside the parenthesis: \[ 144.3 + 47.66 = 191.96 \] Therefore, \[ P = 2 \times 191.96 = 383.92 \mathrm{~m} \] The perimeter of the lot is \( 383.92 \mathrm{~m} \).
03
Understanding Area
The area of a rectangle is calculated using the formula: \[ A = l \times w \] where \( l \) is the length and \( w \) is the width.
04
Calculating Area
Substitute the given values into the formula for area. Here, \( l = 144.3 \mathrm{~m} \) and \( w = 47.66 \mathrm{~m} \). So, \[ A = 144.3 \times 47.66 \] Perform the multiplication to find the area: \[ A = 6875.538 \mathrm{~m}^2 \] The area of the lot is \( 6875.538 \mathrm{~m}^2 \).
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Key Concepts
These are the key concepts you need to understand to accurately answer the question.
Perimeter calculation
Calculating the perimeter of a rectangle is a fundamental concept in geometry. It's crucial to understand it as it applies to many real-life situations such as determining the length of a fence needed to encircle a property. The formula for the perimeter of a rectangle is simple yet insightful:
- Formula: \( P = 2(l + w) \)
- Where \( P \) represents the perimeter, \( l \) is the length, and \( w \) is the width.
Area of rectangle
Understanding how to calculate the area of a rectangle is another key skill in geometry. It helps you know precisely how much space within a boundary is available, which is helpful for planning layout designs, like where to park cars in a parking lot. The technique involves a straightforward mathematical formula:
- Formula: \( A = l \times w \)
- Where \( A \) is the area, \( l \) is the length, and \( w \) is the width.
Mathematics problem-solving
Tackling mathematical problems, especially in geometry, is not just about plugging numbers into formulas. It’s about thinking logically and applying concepts to reach accurate conclusions. Here's a structured approach beneficial when working on shape-related exercises:
- Identify what is being asked. Clearly understand the problem’s requirements before proceeding.
- Equip yourself with the right formulas. Know which mathematical equations relate to the dimensions you're analyzing.
- Substitute the correct values and ensure calculations are accurate.