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Chapter 1: Problem 16

An old manuscript reveals that a landowner in the time of King Arthur held \(3.00\) acres of plowed land plus a livestock area of \(25.0\) perches by \(4.00\) perches. What was the total area in (a) the old unit of roods and (b) the more modern unit of square meters? Here, 1 acre is an area of 40 perches by 4 perches, 1 rood is 40 perches by 1 perch, and 1 perch is \(16.5 \mathrm{ft}\).

Short Answer

Expert verified
14.5 roods, 14668.35 sq meters.

Step by step solution

01

Understand the Measurements and Their Relationships

1 acre = 40 perches by 4 perches, 1 rood = 40 perches by 1 perch, 1 perch = 16.5 ft. We need to convert the livestock area from perches to acres and then add it to the plowed land.
02

Calculate the Livestock Area in Acres

Determine the area of the livestock region in perches: Area = Length 脳 Width = 25.0 perches 脳 4.00 perches = 100 perches. Convert perches to acres. From given, 1 acre = 40 perches 脳 4 perches = 160 square perches. Thus, livestock area in acres = 100 perches / 160 perches per acre = 0.625 acres.
03

Find the Total Area in Acres and Convert to Roods

Total area in acres = Plowed land + Livestock area = 3.00 acres + 0.625 acres = 3.625 acres. Convert acres to roods: 1 acre = 4 roods, so total area in roods = 3.625 acres 脳 4 roods per acre = 14.5 roods.
04

Convert the Livestock Area to Square Meters

First, convert perches to feet: 1 perch = 16.5 ft, so area = 100 perches 脳 (16.5 ft)^2 = 27225 square ft. Convert square feet to square meters: 1 square ft = 0.092903 square meters. Therefore, area in square meters = 27225 sq ft 脳 0.092903 sq meters/sq ft 鈮� 2527.77 sq meters.
05

Convert the Plowed Land Area to Square Meters

1 acre = 4046.86 square meters, thus, area = 3.00 acres 脳 4046.86 sq meters/acre = 12140.58 sq meters.
06

Calculate the Total Area in Square Meters

Total area in square meters = Plowed land in sq meters + Livestock area in sq meters = 12140.58 sq meters + 2527.77 sq meters = 14668.35 sq meters.

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Key Concepts

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

Unit Conversion
Unit conversion is the process of changing a measurement from one unit to another. This exercise involves converting between historical units like acres, perches, and roods to modern units such as square meters. Converting units helps in understanding measurements in a familiar context. Here, we convert perches to acres and then to square meters. Remember that 1 perch equals 16.5 feet, and this is crucial when dealing with ancient measurement systems.
Area Calculation
Calculating area is essential for understanding the size of land or any two-dimensional space. In the exercise, the formula for the area of a rectangle is utilized: Area = Length 脳 Width. For the livestock area, this becomes 25.0 perches 脳 4.00 perches. Understanding how to compute the area helps in visualizing land sizes and performing further conversions effectively.
Historical Measurement Systems
Before standardized units like meters were adopted, various historical measurement systems were used. These systems included units like acres, roods, and perches. For instance, 1 acre = 40 perches by 4 perches, and 1 rood = 40 perches by 1 perch. Understanding these historical units allows us to interpret old texts and documents accurately. The exercise showcases the importance of being familiar with these systems to convert and compare with modern units.
Square Meters
Square meters are part of the metric system and are used worldwide for measuring area. To convert historical units like acres or perches to square meters, specific conversion factors are used. For example, 1 acre = 4046.86 square meters and 1 perch = 16.5 feet. Converting to square meters provides clarity and standardization, especially when dealing with international measurements. This ensures that land sizes are easily understood irrespective of geographical location.
Perches and Acres
Perches and acres are units from historical English measurement systems. A perch measures lengths and areas, consisting of 16.5 feet. Acres, on the other hand, denote larger land areas, equivalent to 43,560 square feet. By understanding the relationship between these units, such as 1 acre = 160 perches, we can easily convert and make sense of measurements in modern terms. The exercise illustrates how these conversions are done step-by-step, enhancing our comprehension of both historical and modern measurement units.

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Most popular questions from this chapter

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