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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 an area of 40 perches by 1 perch, and 1 perch is the length \(16.5 \mathrm{ft}\).

Short Answer

Expert verified
Total area: 14.5 roods; approximately 14666 m².

Step by step solution

01

Calculate the Area of Livestock Area in Perches

The livestock area is given as 25 perches by 4 perches. To find the area in square perches, multiply the length by the width:\[\text{Area of livestock in perches} = 25 \times 4 = 100 \text{ square perches}.\]
02

Convert Acres of Plowed Land to Perches

The plowed land is given in acres. Since 1 acre equals 40 perches by 4 perches, its total area in square perches is:\[\text{Area of 1 acre in perches} = 40 \times 4 = 160 \text{ square perches}.\]Thus, 3 acres in square perches is:\[3 \times 160 = 480 \text{ square perches}.\]
03

Calculate the Total Area in Square Perches

Add the areas of the plowed land and the livestock area:\[480 \text{ (plowed)} + 100 \text{ (livestock)} = 580 \text{ square perches}.\]
04

Convert Total Area from Perches to Roods

Since 1 rood is equivalent to 40 perches by 1 perch, its total area in square perches is:\[40 \times 1 = 40 \text{ square perches}.\]So the total area in roods is calculated as:\[\frac{580}{40} = 14.5 \text{ roods}.\]
05

Convert Perches to Square Feet

Since one perch is equivalent to 16.5 feet, calculate the area of one square perch in square feet:\[16.5 \times 16.5 = 272.25 \text{ square feet}.\]
06

Convert Total Area from Perches to Square Feet

Multiply the total area in perches by the area of one perch in square feet:\[580 \times 272.25 = 157905 \text{ square feet}.\]
07

Convert Square Feet to Square Meters

Since one square meter equals approximately 10.7639 square feet, convert the total area in square feet to square meters:\[\frac{157905}{10.7639} \approx 14666 \text{ square meters}.\]
08

Conclusion

The total area is 14.5 roods in the old unit of measurement and approximately 14666 square meters in the modern unit.

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Key Concepts

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

Area Calculation
Calculating the area of a space involves multiplying its length by its width. This is a fundamental concept in geometry. For instance, to find the area of a livestock plot measuring 25 perches by 4 perches, you multiply these dimensions to obtain:\[ 25 \times 4 = 100 \text{ square perches} \]
Similarly, when calculating the area of land in acres, which given here is 3 acres, each acre equals 160 square perches. Therefore, the total is:\[ 3 \times 160 = 480 \text{ square perches} \]
The total area of these lands combined is then calculated by summing these areas:\[ 480 \text{ square perches (plowed)} + 100 \text{ square perches (livestock)} = 580 \text{ square perches} \]
Using basic arithmetic operations ensures accuracy and helps in converting units efficiently.
Measurement Units
The term 'measurement units' refers to the standards used to quantify physical quantities. In this case, the units cover acres, perches, square feet, and square meters, each used to measure area. Understanding how each unit converts into another is essential. For instance:
  • 1 acre = 160 square perches
  • 1 square perch = 272.25 square feet

Converting between different units involves understanding their relationships, such as:
  • From perches to roods: Since 1 rood is an area of 40 square perches, you convert by dividing by 40.
  • From square feet to square meters: With 1 square meter roughly equivalent to 10.7639 square feet, convert by dividing the total square feet by this number.

This knowledge helps accurately transition between modern and historical measurements.
Historical Units of Measurement
Historical units of measurement like acres and perches were widely used long ago, especially in agricultural and land transactions. These units have deep roots in history, often based on the practical needs of early societies.
  • An acre was originally defined as a day's plowing for a yoke of oxen.
  • A perch, also used as a rod or pole, was a common measure for plot dimensions.

With 1 perch equaling 16.5 feet, understanding these historical units gives insight into past agricultural practices. In today's world where modern units like square meters prevail, converting these old measures is crucial to understand historical records accurately. This way, historical records retain relevance in modern contexts.

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