Answer:
50 mm²
Step-by-step explanation:
The diagonal divides the square into 2 right triangles, with the diagonal as the hypotenuse.
Using Pythagoras' identity in one of the right triangles.
let s be the side of the square, then
s² + s² = 10² = 100, that is
2s² = 100 ( divide both sides by 2 )
s² = 50 ( take the square root of both sides )
s = [tex]\sqrt{50}[/tex] = [tex]\sqrt{25(2)}[/tex] = 5[tex]\sqrt{2}[/tex]
Thus
area = s² = (5[tex]\sqrt{2}[/tex] )² = 50 mm²
