# Calculating the Area of a Rectangle: 400Root & 800Root

• abia ubong
In summary, the conversation is about finding the area of a rectangle with sides represented by power towers, with the values of x and y being the 400th and 800th roots respectively. The area is expressed in whole numbers, using Lambert W-functions. The conversation also includes a discussion on the convergence of the power tower sequence and a reference to MathWorld for further explanation.
abia ubong
how do i find the area of a rectanglewith sides 400root of 400 raised continously to itself like x^x^x^..and 800root of 800 raised also to itself continouslylike y^y^y...
leave answer in whole number not exponent

What do those "..." mean...?I can assume you'd have to evaluate

$$400^{400^{400^{...}}}\cdot 800^{800^{800^{...}}}$$

Daniel.

Do you have any reason to think that such a sequence converges?

Read mathworld's page on the power tower.I'm sure u'll find the upper limit for the convergence interval,that is,of course,if u meant the infinite superpower of 400 and 800 respectively.

Daniel.

Abia, consistent no doubt. I think you mean a power tower like:

"The 400'th root of 400"

$$\sqrt[400]{400}\approx 1.01509$$

I think that's in the range of convergence.

Edit: The 800 one too for that matter.

Last edited:
area of rectangle with length x^x^x^x^x...
and breath y^y^y^y^y^y... where x is 400^ 1/400 and y is 800^ 1/800.
leaving answer in whole number not decimal or exponent

abia ubong said:
leaving answer in whole number not decimal or exponent

Hello Abia. Yea, leaving it in whole numbers . . . hum . . . how about expressing the power towers in terms of Lambert W-functions (which can be done and in whole numbers), and in this way then the area is just a product of two such expressions.

do not understand
pls explain

mathelord said:
do not understand
pls explain

Check out Power Towers, and Lambert W-functions in MathWorld. Try that first.

## 1. How do you calculate the area of a rectangle?

To calculate the area of a rectangle, you simply multiply the length by the width. The formula for area is A = length x width.

## 2. What is the significance of the numbers 400Root and 800Root in calculating the area of a rectangle?

The numbers 400Root and 800Root are most likely referring to the length and width of the rectangle. These numbers could represent the square root of 400 and 800, respectively, which would be the length and width of the rectangle.

## 3. Is there a specific unit for the area of a rectangle?

Yes, the area of a rectangle is typically measured in square units, such as square inches, square feet, or square meters.

## 4. Can you use the same formula to calculate the area of a square?

Yes, the formula for calculating the area of a rectangle can also be used to calculate the area of a square. Since a square has four equal sides, the length and width will be the same, making the formula A = side x side.

## 5. How do you calculate the area of a rectangle if the length and width are not given?

If the length and width of the rectangle are not given, you will need to measure them first. You can do this by using a ruler or measuring tape. Once you have the measurements, you can plug them into the area formula A = length x width to calculate the area.

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