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If "a" is the side length of a square, then the square of its diagonal is
a^2 + a^2 = 2a^2, according to Pythagoras.
From the other side, the area of such a square is a^2.
So, to calculate the area in your case, you need to square the diagonal and then divide it by 2:
Area = = = 32 square units.
Answer. The area of the given square is 32 square inches.
Solved.
Another way to solve it is THIS :
The diagonals divide the square in 4 congruent right angled triangles with the legs of the length 4 unit each.
So the area of each such triangle is = 8 square units.
Then the area of the entire square is 4 times it, i.e. 4*8 = 32 square units - the same answer.