The Geometry of the Vegetable Garden

Harvest from the vegetable garden
A few answers to some questions about my vegetable garden.

How big is it?

Follow along and I’ll tell you how big it is.

For those who studied geometry “some time ago”, a refresher on shapes…

My vegetable garden is four-sided, so it is technically a quadrilateral, which is what any four-sided shape is called. (Are you starting to get a little nervous that there might be a quiz, like in school?)

Because two sides of the garden, the north side and the south side, are parallel, my quadrilateral shaped garden is technically a trapezoid. Because the other two sides, which aren't parallel, are the same length, it is actually an isosceles trapezoid. If I remember high school geometry correctly, I think the sum of the four interior angles should be 360 degrees, but I won’t swear to that.

So what is the area, in square feet, of an isosceles trapezoid, given that the two parallel sides are approximately 50’ and 67’ and the other two sides, which are not parallel, are about 23’ feet each? (I use “approximately” and “about” deliberately because I measured quickly which means I could measure again and end up with completely slightly different measurements.)

Get out your protractors, slide rulers, and scientific calculators!

Or figure out the answer the way I did.

There is a rectangle within that isosceles trapezoid that is 23’ x 50’, approximately, which is 1,150 square feet.

That leaves two triangles, one on each end of the garden that if you put them together to form another rectangle, that rectangle would be about 23’ x 8’, roughly, maybe, am I thinking about this in the right way? That’s about another 174 square feet, which I’ll round to 175 square feet.

Add that 175 square feet to the 1,150 square feet of the other rectangle and you have 1,325 square feet of vegetable garden space.

That’s a nice size for a vegetable garden, if I do say so myself.

If I lay out the garden with some thought, hopefully over half of it will be raised beds and not paths, giving me at least 650 square feet of planting area. Previously, I had 492 square feet of planting area.

What about that apple tree in the center of the garden?

Why did I plant that apple tree there? It made sense at the time to plant it in the approximate center of the garden, but now that I see the clean slate that I have, the apple tree seems to be in the way. I don’t like it there, and it has never produced any decent apples.

It’s time to invoke one of the secrets to achieving happiness in your garden, the first secret.

Do you remember what it is?

Grow the plants you love.

(Aren’t you all lucky I’m not making you take a quiz?)

I don’t love that apple tree or the variety of apples it should produce.

Don’t look. Turn your head if you are squeamish.

It will take just a few minutes to cut down that little apple tree with my reciprocating saw.

Then the entire 1,325 square feet, give or take, of vegetable garden space will truly be a clean slate.

(We garden fairies just added this picture to this post.  Why Carol didn't include it, we'll never know!)
By the way, Dr. Hortfreud says that this garden is .030417 acres... in other words 3% of an acre. That makes it seem very tiny. It's all relative, she says.


p3chandan said…
To tell you the truth Carol, I really cant figure out the size or shape of your garden..failed my maths! why not show me the photos?
Layanee said…
Oh yes, pictures please.
Fairegarden said…
Some of us are visuals, and need pictures or diagrams, but I did follow your calculations if the geometry in my brain is cobwebby. That is a lot of space! Goodbye to the underperforming apple tree. Perhaps the wood could be used for something, do you have a smoker cooker thingey?

Ok, I'm the first to admit that math is not my long suit, although I did fairly well with geometry, because it was visual and concrete (until we got into tangents). But if the north and south sides are parallel and the east and west sides are the same length (parallel? non parallel?).

I couldn't help but notice the ad for the desperate landscape guy on your site next to the column.

But, you go girl w/the tough love on the apple tree.
Melissa said…
Who knew that math could possibly be so important to be used in gardening. Oh wait the school did. Sad about the apple tree but if it doesn't make you happy the rest of the garden won't be happy. Besides, maybe you'll end up with something better for those Garden Fairies to live in.
Gail said…
I can't wait to see the beds in the garden~I need photos, am terrible at visualizing. gail
I did better by counting the panels in your privacy fence to give me the idea of how large your veggie garden is. It is a nice size. Maybe you could do a couple of apple trees espaliered on that fence. That way they wouldn't be in the middle giving off shade where you don't want any shade. It is so exciting. Do you have a diagram or do you just go out and start putting in stakes and twine to show where you want the beds?
I'm looking forward to seeing the raised beds! What material are you planning on using? I'm shifting ours to stones as I can afford to.
karen kennedy said…
Gosh at this early hour math eludes me, oh who's kidding who, math always eludes me. I am a firm believer of Jimmy Buffett's song "Math Sucks". However I was forced into some Geometry when involved in hot air ballooning so it sort of made sense. So I'll just second Jo Ellen, You go girl and take out that Apple tree. I have a crab apple that you can work on next.
I must say that math was not one of my strong suits and therefore during your description my eyes glaced over. However, I am sure that your garden will be very productive and that is what counts. V
Sissy said…
I don't excel at math, either, but if it's like my garden, it seems too small. Till it's time to weed!
Kathy said…
I would do better seeing a diagram, or floor plan, of the vegetable garden, maybe after you plan out the beds.
Anonymous said…
Now it is time for the graph paper, but remember to save space for 'points of interest.' Wise move to remove an unproductive tree. Have fun, can't wait to see the finished project and all the goodies.
Leslie said…
I was never great at math but your description seemed pretty clear to me...and very clever the way you broke it down for figuring size. So your lot lines are the 2 shorter sides? I think it's smart to loses the apple tree...but will you have some other central focal point? Raised herb bed? Art? Small arbor for pole beans/peas? This is so much fun!
Charles said…
Dang! I wish I could write with your wit, humor and imagination. That's exactly why I'm your eager reader.
ProfessorRoush said…
It would be so much easier if we just expressed square area in strawberry plants. My vegetable garden has an area of approximately 1200 strawberry plants.
Annie in Austin said…
Our house lot is a trapezoid so we've done similar math calculations here, Carol. (That was the royal 'we'... I posed the question and let the resident mathematician solve it.)

1335 square feet of vegetable garden! 650 square feet of actual planting area! Wow... can't quite get up to 100 square feet total here, even if I add in things like the herb troughs on the patio. You will have so much fun!

Annie at the Transplantable Rose
Susan in NC said…
You'll be jealous: I have 1340 square feet of beds, plus walk ways, fruit trees, blueberry and currant bushes, compost piles, burn pile, chicken house, chicken run, etc. It's a great luxury to live in the country.

Don't apples need to have at least 2 types growing close enough to cross-pollinate in order to bear? Maybe that's why your lonely little tree isn't producing much.
Michele said…
Oh, my two loves, math and gardening! Loved this post. Regards, Michele