Question

A square its diagonal length = 12cm then its area =

Answer 1

72 sq cm

Explanation:

For any rectangle, the diagonal is the hypotenuse of the right triangle formed by the base of the rectangle(b) and the height (h) of the rectangle

By the Pythogorean formula

`d^(2) = b^(2) + h^(2)`

where d is the diagonal

For a square, all sides are equal so b = h = a and we get the formula

`d^(2) = a^(2) + a^(2) = 2a^(2)`

`a^(2) = d^(2) /2`

In this case we have d =12 so

`a^(2) = 12^(2) /2 = 144/2 = 72`

But for a square of side a, the area is
`a^(2)` so 72 is the area

Answer 2

72 square cm

Explanation:

Area of square:

`\sf \boxed{\bf Area = (d^(2))/(2)}` , here d is the length of the diagonal

`\sf =(12* 12 )/(2)\\\\ = 6*2\\\\= 72 \ cm^2`