## Dimensions Calculation for a "Pyramid" Inside a Rectangle (Terrarium Setup)

## Dimensions Calculation for a "Pyramid" Inside a Rectangle (Terrarium Setup)

(OP)

Good day!

I do not work in engineering but i am a librarian with a new passion to terrariums.

I would need some advice for calculating the measurements for the sides of a flat top pyramid inside a rectangular terrarium.

Added is some screenshots of my 3D-model to show what im working with. The terrarium is 75x40x40cm and the square at the bottom of the pyramid will be 15x15cm or 20x20cm.

So what im doing is im building a 2 level aquarium/terrarium. Bottom level will be filled with water and the levels divided by a "flat top pyramid" shape made out of plexiglass/polycarbon sheet 3mm thick.

Because the pyramid is upside down and i need some sort of structural integrity for it to be stable i decided to level it (will have a pump inside it too).

My problem and question is. What is the method/formula to get outside measurements of the four separate pyramid walls? "The terrarium is 75x40x40cm and the square at the bottom of the pyramid will be 15x15cm or 20x20cm."

Might be something obvious im just not realizing but i tried to search online for information but english isnt my first language and im not sure what terms to use for finding my answer.

So this is why i figured an engineering forum might be my best chance!

Thank you in advance!

I do not work in engineering but i am a librarian with a new passion to terrariums.

I would need some advice for calculating the measurements for the sides of a flat top pyramid inside a rectangular terrarium.

Added is some screenshots of my 3D-model to show what im working with. The terrarium is 75x40x40cm and the square at the bottom of the pyramid will be 15x15cm or 20x20cm.

So what im doing is im building a 2 level aquarium/terrarium. Bottom level will be filled with water and the levels divided by a "flat top pyramid" shape made out of plexiglass/polycarbon sheet 3mm thick.

Because the pyramid is upside down and i need some sort of structural integrity for it to be stable i decided to level it (will have a pump inside it too).

My problem and question is. What is the method/formula to get outside measurements of the four separate pyramid walls? "The terrarium is 75x40x40cm and the square at the bottom of the pyramid will be 15x15cm or 20x20cm."

Might be something obvious im just not realizing but i tried to search online for information but english isnt my first language and im not sure what terms to use for finding my answer.

So this is why i figured an engineering forum might be my best chance!

Thank you in advance!

## RE: Dimensions Calculation for a "Pyramid" Inside a Rectangle (Terrarium Setup)

## RE: Dimensions Calculation for a "Pyramid" Inside a Rectangle (Terrarium Setup)

Also, do you want it to be symmetrical? It looks offset in your sketch.

## RE: Dimensions Calculation for a "Pyramid" Inside a Rectangle (Terrarium Setup)

Let c = (a-b)/2

then h' = (h

^{2}+c^{2})^{0.5}EDIT: If a = 40, b = 20 and h = 75/2 = 37.5,

then c = (40 - 20)/2 = 10

and sloping height h' = (10

^{2}+ 37.5^{2})^{0.5}= 39.1BA

## RE: Dimensions Calculation for a "Pyramid" Inside a Rectangle (Terrarium Setup)

SnailBait, if you have modeled the thing, how do you not have dimensions? BTW, probably more suited to the Hobbies forum.Regards,

Mike

The problem with sloppy work is that the supply FAR EXCEEDS the demand

## RE: Dimensions Calculation for a "Pyramid" Inside a Rectangle (Terrarium Setup)

RTFM is not an answer and is of little help... thanks BART.

BART may not hang out there...

Dik

## RE: Dimensions Calculation for a "Pyramid" Inside a Rectangle (Terrarium Setup)

The problem with sloppy work is that the supply FAR EXCEEDS the demand

## RE: Dimensions Calculation for a "Pyramid" Inside a Rectangle (Terrarium Setup)

Isn't this all geometry and trigonometry?

## RE: Dimensions Calculation for a "Pyramid" Inside a Rectangle (Terrarium Setup)

^{2}+ 2c^{2})^{1/2}For a, b, h = 40, 20, 37.5 respectively,

c = 10; H = 40.08 (edge shown in retired13's sketch)

h' is the actual width of plexiglass required for each wall.

N.B. For a good fit, plexiglass edges must be cut to the proper angle.

BA

## RE: Dimensions Calculation for a "Pyramid" Inside a Rectangle (Terrarium Setup)

## RE: Dimensions Calculation for a "Pyramid" Inside a Rectangle (Terrarium Setup)

Don't have time to check everything now, going picking mushrooms. But I will do so later and respond better then!

## RE: Dimensions Calculation for a "Pyramid" Inside a Rectangle (Terrarium Setup)

For the hight im thinking eighter 12 or 14cm not 100% sure yet.

SnTMan - I do have general dimensions but I used Tinkercad to model it and I didn't figure out how to get measurements of the angled parts. It doesn't show them automatically and the ruler tool didn't work as I thought it would.

Thank you all for the pictures and drawings! This should really get me started!

Will see how well I get the plexiglass edges fixed. I'm working with limited tools. Ruler, boxcutter and hand held electric belt sander. Shouldn't be a problem!

## RE: Dimensions Calculation for a "Pyramid" Inside a Rectangle (Terrarium Setup)

## RE: Dimensions Calculation for a "Pyramid" Inside a Rectangle (Terrarium Setup)

Below is a plan and elevation of the terrarium. The truncated rectangular pyramid is shown in green. The plexiglass wall dimensions are shown in orange.

Note: sqrt means square root.

EDIT: Corrected errors in sketch

BA

## RE: Dimensions Calculation for a "Pyramid" Inside a Rectangle (Terrarium Setup)

Got to think like an artist, not a structural engineer.

## RE: Dimensions Calculation for a "Pyramid" Inside a Rectangle (Terrarium Setup)

When one has grabbed the fundamental, no mater how it is shaped, just follow the basics. Straight lines, no curve though.

## RE: Dimensions Calculation for a "Pyramid" Inside a Rectangle (Terrarium Setup)

## RE: Dimensions Calculation for a "Pyramid" Inside a Rectangle (Terrarium Setup)

## RE: Dimensions Calculation for a "Pyramid" Inside a Rectangle (Terrarium Setup)

Might be fun to make the tank a trapezoid, rhombus or irregular pentagon.

BA

## RE: Dimensions Calculation for a "Pyramid" Inside a Rectangle (Terrarium Setup)