Question

If the diagonal of the
square is 12 √ 6cm, find the
area?

Answer 1

Below in bold.

Explanation:

The diagonal forms 2 right triangles in the square,

Applying the Pythagoras Theorem to a triangle:

(12√6)^2 = x^2 + x^2 where x is the side of the square.

144*6 = 2x^2

x^2 (which is the area of the square)

= 144*6 / 2

= 144*3

= 432 cm^2.

Answer 2

432 cm²

Explanation:

Diagonal of Square = √2a

=> 12√6 = √2a

=> a = 12√6 / √2

=> a = 12√3 ( because √6 can be written as √2 × √3 , so √2 and √2 cancel out)

Now the Area = a²

= (12√3)²

= 144 × 3

= 432 cm²