# What is the tv screen area in square inches of a

• MHB
• loukatz
I learned it in school and have been practicing for many years. Now, to summarize the conversation:In summary, we discussed the ratio of a big screen TV, which is 16:9, and how TVs are advertised by their diagonal length. We also derived a formula to find the screen area in square inches as a function of the diagonal. This formula is A = (144/337) * d^2, where d is the diagonal length. This formula was derived using the Pythagorean theorem and the given ratio.
loukatz
Assume that the ratio of a big screen TV is 16:9. TVs are advertised by their diagonal (sp?) length. What is the screen area in square inches of a:

a) 40 inch TV

b) 60 inch TV

c) 65 inch TV

d) 80 inch TV

e) 86 inch TV

Show the formula (equation) that you used.

Thank you

Let's let $x$ be the width of the screen and $y$ be the height, and so we have:

$$\displaystyle \frac{x}{y}=\frac{16}{9}\implies y=\frac{9}{16}x$$

Let $d$ be the diagonal measure of the screen...by Pythagoras we have:

$$\displaystyle x^2+y^2=d^2$$

Substituting for $y$, we have:

$$\displaystyle x^2+\frac{81}{256}x^2=d^2$$

$$\displaystyle \frac{337}{256}x^2=d^2\implies x^2=\frac{256}{337}d^2$$

Now, the area $A$ of the screen is:

$$\displaystyle A=xy=\frac{9}{16}x^2=\frac{144}{337}d^2$$

Now you have a formula to find the area as a function of the diagonal. :)

I'm amazed by this forum. How do you know all that?

Last edited:

## 1. What is a TV screen area measured in?

A TV screen area is typically measured in square inches.

## 2. How do you calculate the TV screen area?

To calculate the TV screen area, you can measure the length and width of the screen in inches and then multiply them together to get the total number of square inches.

## 3. What is the average size of a TV screen?

The average size of a TV screen varies, but it is typically around 32-55 inches diagonally, which would equal to a screen area of approximately 512-2,425 square inches.

## 4. Is the TV screen area the same as the screen resolution?

No, the TV screen area and screen resolution are not the same. The screen resolution refers to the number of pixels on the screen, while the screen area is the physical measurement of the screen in square inches.

## 5. Does the TV screen area affect the viewing experience?

Yes, the TV screen area can affect the viewing experience. A larger screen area can provide a more immersive viewing experience, while a smaller screen area may be more suitable for smaller spaces or individual viewing.

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