Question

Square ABCD has a diagonal of 8 inches long. How many square inches is the area of the shape?

Answer 1

If you look carefully, that diagonal would be the Hypotenuse and the arms of the Square (which is equal in magnitude) would be the shorter sides.

Then, According to Pythagoras Theorem,
a² + b² = c²
2a² = 8²
a² = 64/2
a = √32

Now, Area = Side²

So, A = (√32)²
A = 32 in²

In short, Your Answer would be; 32 in²

Hope this helps!

Answer 2

The diagonal of any square always occurs in a ratio of
`\sqrt2:1` relative to the square's sides. That means if
`s` is the side length, then
`\sqrt2s=8` gives the length of the diagonal. It follows that
`s=\frac8{\sqrt2}`.

Then the area of the square is


`s^2=\left(\frac8{\sqrt2}\right)^2=\frac{64}2=32` square inches