Question

the diagonal of square is 10cm find its area

Answer 1

Given AC=10cm

ABC and BCD are right angle triangles....

apllying pythagarus theorem

AC2=AB2 + BC2

but in a square all sides has equal length

102=2AB2

AB2= 100/2

AB2=50

AB = root(50)

area of a square = a2

where a = side of the suare

area= AB2

=> [root(50)]2

=> 50 cm2
Hope it's help u

Answer 2

Let the side of the square be= a

Using Pythagoras Theorem,  
a^2 + a^2 = 10^2
2*(a^2) = 100
a*a = 50 cm^2 = area of triangle