Answer:
100 square units
Explanation:
You want the area of a square that has a diagonal length of 10√2.
Rhombus
A square is a rhombus, with perpendicular diagonals. A square is also a rectangle, so its diagonals are the same length. The area of a rhombus is half the product of its diagonals:
A = 1/2(10√2)² = 1/2(200) = 100 . . . . square units
The area of the square is 100 square units.
Side Length
The diagonal of a square is √2 times the length of one side, so the diagonal being 10√2 means the side length is 10. The area of a square with a side length of 10 is ...
A = s² = 10² = 100 . . . . square units