Find the Diagonal of a Square from Area | Geometry

How do we find the diagonal of a square when given the area? We'll solve this geometry problem in today's video math lesson!

This is a fairly straightforward problem, and unsurprisingly it requires us to use the Pythagorean theorem! If we have a square that has area 25, for example, we know the side lengths of the square are the square root of 25 - since the area is the side length squared. Thus the square has sides of length 5. Two sides of a square that intersect in a right angle can then be treated as the leg lengths of a right triangle formed by those sides with the diagonal of a square (the video will make this more clear with a diagram). To finish solving the problem we just apply the Pythagorean theorem to find the diagonal length of the square, which is the hypotenuse of our right triangle!

We could use this method to create a general formula (the formula would be, given an area A of a square, the diagonal d is d = sqrt(2A) ). But I'd recommend just solving the problem whenever necessary, rather than memorizing a formula, because it is a quick problem to solve once you know how to do it.

Note that this method doesn't work for rectangles in general since a rectangle may not have sides of equal lengths. For example, if a rectangle had an area of 6, it could have sides of 3 and 2 or 6 and 1, just to name two possibilities. But a square with area 6 must have sides of length sqrt(6).

I hope you find this video helpful, and be sure to ask any questions down in the comments!

+WRATH OF MATH+


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[shadowofwargamer]

I live in Egypt and I haven't seen any one teaches as you good job

[alterboytn]

that really helps i was struggling with that type of question for a while

[daoudmirza.mviewsmontha]

Thanks alot i was having trouble with these problems and this really helped me out. Nice job 👍

[astrqun]

*HELP ME*

BTW amazing video! Very helpful and very clear. Love how you make i more fun than it seems!

[dawsontate]

A helpful tip, is that for a square, your diagonal will always be the base number square root 2.
For example a square with side length 5 will have a diagonal that is 5 square root 2. A square with side length 4 will be 4 square root 2. This goes for all 45-45-right triangles. Bases are equivalent and the hypotenuse is base length square root 2

[shreoseechowdhury]

Thank you much! I have my exams very near and I was struggling with these type of question, I badly needed this solution. 😭❤️

[kimkimbada]

I couldn't understand how my teacher was explaining it, but you made it much easier, thank you very much

[eshashirali]

Hey could you help me by teaching us how to get the area from the diagonal

[jonatzy]

thank you i wouldt have ever finished my modules if it wasn't for you thanks

your good at explaining again thank you. you were very helpful

[knaj]

Great maths teacher couldn’t find any maths teacher doing this but found you and my god you explain it a fascinating way thank you again

[Dragon-Slayr]

Is this how they will use the ball on the ardvark nose to use it as a turret with the club hiding inside the ball but the ball is the pelican boat with 2 diagonal squares

[sanjaysingh-nszt]

I live in England
I think you teach me best

[priyankagupta]

Finally don't need to struggle with these types of freaking questions THANKS !!

[cheesecake]

You teach better than my math teacher :p

[jennifermarieherron]

Use cloth. lay it flat, fold, find highest stress points, adapt each stress.

(instead of adapting the entire length for each stress by cutting new holes).

[dAnDeLiOnS_]

Can you make the same kind of video except that we have to find the diagonal of a rectangle?

[NinjaBrickz]

the first problem was the same one I was stuck on😄thanks😁

[mohamedtarek]

Iam from egytp i very lucky to see your explaintion about diagonal

[mabimabi]

Dude your teaching is as great as your posture

[dextershutt]

How did you come up with the 5.66 cm? I’m following everything else except how you came up with the last answer