Any math lovers here?

[jnicholes]

Hello,

I am posting this because I want some input from other people who like math. I also like to share math stories.

I was working at Lowes recently helping a customer with bricks, and he asked a question about how many bricks would fit in a certain area with a certain shape. I helped him with mathematics and he was astounded. This did pose a question in my mind, however. The question was, "How do you find the area of a pentagon?"

I was doing math trying to figure it out and trying to see if there is an equation to do it easy. After a LONG time experimenting with equations, about five days, I found the answer and was able to prove it correct with an internet polygon calculator. The equation is this.

2.3776 multiplied by the radius squared equals the area of the pentagon.

I dont know how, but the answers I get with this equation match the online polygon calculators answer, no matter the radius.

Here is the calculator I used:

https://www.blocklayer.com/trig/polygonseng.aspx

I wanted to share this and see if other math lovers wanted to share and talk about math stuff on this thread.

Jared

 

[Starwise]

Made me dust off the old trig lessons. For practical purposes for pavers and such you can use 1.75 (1 3/4 for those using imperial) times side squared. The actual is 1.72 x side squared. That is if you have an equal pentagon. For all polygons the equation is perimeter x apothem / 2. Apothem is radius measured to the tangent of the side in relation to the center of the polygon.

Btw love that site, that is now bookmarked right next to right angle calculator I keep using when fabricating stuff.

 

[Justso]

The only math I know is starting with one chicken and ending up with 7, no really six and a half because one is a bantam, and actually you're going to be getting two more soon so that total is quite right either. And besides that another Coop happened to show up in my yard so all of this could double...

 

[Starwise]

The only math I know is starting with one chicken and ending up with 7, no really six and a half because one is a bantam, and actually you're going to be getting two more soon so that total is quite right either. And besides that another Coop happened to show up in my yard so all of this could double...

That multiplication is running rampant, you forgot brackets to keep it contained.

 

[jnicholes]

Hello,

@Starwise, I learn something new every day! I see where you are coming from with the area equation, and I appreciate the input!

However, my equation still gets the right answers according to the calculator. I dont know why. I did the equation with about 5 different lengths of radius, and according to the online calculator, which I used to check my work, I was right. I got the same answer.

For example, a radius of 3 feet. 3 feet squared is 9. Multiplied by 2.3776, the answer is 21.4 according to the equation. The online calculator says the same.

Another example. 5 foot radius. Five squared is 25. 25 times 2.3776 is 59.44. Online calculator says the exact same.

I dont know why. Do you know why?

A lot of times, a customer asks me, "How many of these pavers do we need for this area?" I LOVE those questions, and they love seeing me do the math on paper.

Jared

 

[aim30]

To find the area of a pentagon, I would split the figure in 2. Find the area of the base (trapezoid) with A=1/2 (b1 + b2) × h, and add the area of the top (triangle) with A=1/2 b x h.

 

[jnicholes]

Hello,

@aim30, That’s what I did before. I was just thinking to myself, “is there an easier and quicker way to do this?“

Jared

 

[Starwise]

“is there an easier and quicker way to do this?“

Divide the pentagon into 5 isosceles triangles. Area of each triangle is half the base length (half the side of the pentagon) times the height of the triangle (radius of the pentagon measured to the mid-point of the side). Multiply by 5.

5 x h x b/2

 

[jnicholes]

Hello,

I am trying to say I get the same answer on the calculator when I do this equation.

2.37765 times the radius squared.

I don’t know why, but it works.

Jared

 

[jnicholes]

Hello,

Haven’t posted in a while due to some problems where I’m at.

I was looking at your equation, and I decided to compare your equations result with the results from my equation. This is the result.

The area equation which is (5/2)r^2sin(72) and the equation I came up with, which is 2.37765r^2 have the same answer. I just did the math on paper, and both are coming up with the same answer.

We were both right, both our equations work.



Jared