An old manuscript reveals that a landowner in the time of King Arthur held 2.74 acres of plowed land plus a livestock area of 24.3 perches by 5.47 perches. What was the total area in (a) the old units of roods and (b) the more modern units 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 ft.

a) 15.23 roods

b) 15487.15 m²

Explanation:

Given:

Area of plowed land = 2.74 Acres

Livestock area = 24.3 perches by 5.47 perches

Now,

a) Total area = 3 acres + (24.3 perches + 5.47 perches)

also,

1 acre = 40 perches by 4 perches

thus,

Total area = 3 * (40 perches * 4 perches) + (24.3 perches + 5.47 perches)

or

Total area = 480 perch² + 132.921 perch²

Or

Total area = 612.921 perch² ... (1)

Also,

1 rood = 40 perches * 1 perches = 40 perch²

thus,

1 perch² = 1/40 rood

therefore,

612.921 perch² = 612.921 * 1/40 rood = 15.23 roods

b) Now 1 perch = 16.5 ft

thus,

1 perch² = 16.5² ft² = 272.25 ft²

also 1 m = 3.28 ft

thus,

1 ft = 1/3.28 m

or

1 ft² = (1/3.28 m) ² = 0.0929 m²

Now

from (1) we have

Area = 612.921 perch²

612.921 perch² = 612.921 * 272.25 ft² = 166617 ft²

also

166617 ft² = 166617 * 0.0929 m² = 15487.15 m²