What is the area of a square field whose diagonal is 40 meters?

800 sq m

According to the question:

\(\sqrt {2}\) a = 40

a = \(\frac{ 40}{\sqrt {2} }\)

rationalizing the denominator:

a = \(\frac{ 40}{\sqrt {2} }\) x \(\frac{ \sqrt {2}}{\sqrt {2} }\)

a = \(\frac{40 }{2}\) x \(\sqrt {2}\) 

a = 20 x \(\sqrt {2}\) 

Side of the square =  20 x \(\sqrt {2}\) 

Area of the square = (side)²

Area of the square =  (20 x \(\sqrt {2}\) )²

Area = 800 cm²