"using Pythagoras, you find the length of either of the two sides.
For example, if the diagonal is = 5
Then square it = 25
Then Half it (since both of the other sides of one of the triangles are equal) = 12.5
Then Square Root it = sqrt(12.5)
The length of one side is sqrt(12.5)
So now you can just square it and the area is 12.5
Hope that makes sense"
Actually there are steps here you don't need. Use the equation: A= (d^2)/2 Where d=diagonal length. You don't need to square root it then square it again. That would only make sense if you wanted to find the side length, but in that case all you would have to do is divide the diagonal by the square root of 2, which will also give you the side length, but in a much easier way.
Using Pythagoras: diagonal² = side² + side² = 2 × side² → side² = diagonal² ÷ 2 area = side² = diagonal² ÷ 2 → diagonal² = 2 × area → diagonal = √(2 × area) = √(2 × 36) = 6√2 ≈ 8.49
Using Pythagoras' theorem: 8 times the square root of 2 which is about 11,3137085 cm
Using Pythagoras' theorem it is 10 times the square root of 2 which is about 14 feet
Using Pythagoras' theorem the longest exterior diagonal is 19.209 cm to 3 dp
Using Pythagoras; theorem it is 12 times square root of 2 which is about 17 cm rounded to the nearest integer
It depends on the relationship between the triangle and the square!
Using Pythagoras: 322+362 = 2320 and the square root of this is the length of the diagonal
Using Pythagoras' theorem the answer is equal to the square root of 2.
About 5.656854249 cm using Pythagoras' theorem: 2x2 = 64
Using Pythagoras's theorem, you will find that the diagonal is sqrt(2) = 1.4142 cm (approx),
By using the Pythagoras theory, which is a2 + b2 = C2 A and B being each length and c being the diagonal.
Cool question ! Answer - half it then cube it to prove it - an example for you if cube diagonal (not square diagonal) is 100, then using pythagoras theorm the square diagonal = 70.71068, If square the square diagonal = 70.71068, then using pythagoras theorm the side length = 50 therefore the volume = 50 ^ 3 = 25000 units works with any numbers
That depends how exactly the measurements of the sides are - and how exactly the "right angle" is really a right angle. If the measurements are exact, then, yes, you can also calculate the diagonal exactly - using Pythagoras' Theorem..................................................................................................................................Improved Answer:No it's not possible to find the accurate length of the diagonal of any square using Pythagoras' theorem because the answer will always be an irrational number which can never be determined just like the value of pi in a circle.
The side length of the square is about 3.54 units using Pythagoras' theorem for a right angle triangle
Firstly you need to work out the length of a side. Using Pythagorean Theorem for a right angled triangle a2+b2=c2 where a = the length, b = height & c = diagonal since c = 8 and a = b are the same 2a2 = 64 a2 = 32 a = 5.657 cm since the area of the square is a2 then area = 32cm2
Using Pythagoras' theorem which says that the square on the hypotenuse (in this case the diagonal) is equal to the sum of the squares on the other two sides (which in the case of a square would be equal in length). so if the diagonal measured 10 units, the square on the diagonal would be 100 square units. And as this = 2*the squares on the other sides, the square on one side would be 100/2 = 50 square units. As a square has sides of equal length the square on one side is actually the area of the square. i.e. the area of a square with a diagonal of 10 units is 50 square units. or generically the area of a square with a diagonal of length 'x' = (x2)/2
Each side of the square is 20 inches and by using Pythagoras' theorem its diagonal is 20 times the square root of 2 which is about 28.284 inches rounded to 3 decimal places.