Number

[Guest]

An acre of land is to be planted with trees. The trees are to be placed 4 feet apart. Determine number of trees.

My attempt :

An acre = 43,560 square feet, 4840 square yards.

43560 / 4 = 10890 trees

Where did I miscalculate ?

[Guest]

I think you have to multiply by 4 instead of dividing.

[Guest]

43560 x 4 = 174,240

Seems like a lot of trees on just an acre.

[Guest]

the first post just considered a strip one foot wide and a tree planted every 4 feet

If it is a square acre, it will be 208 feet by 208 feet
That gives 52 trees by 52 trees
That gives 2704 trees total

.......Simple.......

[Guest]

I have located another answer:

2722.5

How was this answer obtained ?

[Guest]

how was your answer obtained.

what does half a tree look like

[Guest]

"how was your answer obtained."

I don't know.

[Guest]

"what does half a tree look like"

Non- existent.

[Guest]

This is the correct answer, until someone proves it wrong by posting a better answer.
Properly set out to show the method of solution.

If it is a square acre, it will be 208 feet by 208 feet
That gives 52 trees by 52 trees
That gives 2704 trees total

.......Simple.......

[Guest]

I have a question:

The problem just indicates the area is an acre with trees planted 4 feet apart.

What if the acre was rectangular or circular in shape, with trees still planted at 4 feet apart ?

Just curious. Thanks.

[Guest]

There are alot of different shapes of rectangle that have an area of an acre.
Surely you can work this out yourself from the method given in the previous post for a square acre.
Decide on a width in feet that is divisible by 4
Divide it into the square feet in an acre to get the length
Then it will be the number of trees in a row multiplied by the number of rows.

And do a similar circular calculation for the circular acre

What about a Triangular Acre, or a Parallelogram acre, Elipical Acre, Trapezoidal Acre, Hexagon Acre, Octagon Acre
,

[Guest]

What about just planting them in a field that is an irregular shape

And if I plant 4 in a square 4 feet apart, they are more than 4 feet apart when measured diagonally across the square

[Guest]

Further to my earlier calculation for a Square Acre.......
This is my solution for an Equilateral triangular Acre of land............

For a Equilateral Triangular plot of land and,
Trees planted at corners of equilateral triangles having sides of 4 feet.

Area of plot = 0.5 x a x b x sin of the angle

43560 = 0.5 x a x b x Sin 60

43560 / (0.5 x Sin 60) = a x b

100579.5 = a x b

a and b are equal so take sq root of 100579.5

gives length of side of plot = 317 feet

4 feet apart, divide by 4, gives 79 trees in the rows at the outer edge

there will be 1 tree less in each successive row....arithmetic series.

So find the sum of 79 terms from 1 to 79 having a common difference of 1

Sum = (79/2)x(2x1 + 1(79-1))

Sum = (79/2)x(80)

Sum = 3160

Actual area of land = 0.5 x 79 x 4 x 79 x 4 x 0.866

Actual area of land = 0.5 x 316 x 316 x 0.866

= 43239 sq feet

difference from 1 acre = 43560 - 43239

= 321 sq feet

Which is a strip approx 1 foot wide along one edge of the triangular plot
and not wide enough to plant more trees giving 4 feet spacing

So 43239 sq feet = 4804 sq yards ......99% + of the acre planted

Total Number of trees for Equi. Triangular Plot is 3160.

This is probably the most dense planting you can obtain with 4 feet spacing in all directions ........

...............................Simple.................................

[Guest]

And...... For a rectangular plot of length twice its width
and trees planted 4 feet apart at corners of 4 feet squares

Dimensions 148 feet wide x 294 feet long

Gives 37 trees x 73 trees

Gives 2701 trees total

............................Simple...................

[Guest]

Thanks.