Question

Find the area of the figure.
16

Answer 1

The area of the square with a diagonal of 16 cm is 8 unit sq

To find the area of a square when the diagonal is given, first remember that in a square, the diagonals are equal and they intersect at 90 degrees, dividing the square into two congruent right-angled triangles.

The diagonal is the hypotenuse of each triangle.

Since we have the length of the diagonal, we can use the Pythagorean theorem to find the length of one side of the square.

Let the side of the square be a.

Then, the diagonal d will be d = a
`√(2)` (because in a 45-45-90 triangle, the hypotenuse is
`√(2)` times the length of a leg). If the diagonal (d) is 16 cm, then:

`a√(2) = 16`

`a = (16)/(√(2))`

`a = (16)/(√(2)) * (√(2))/(√(2))`(rationalizing the denominator)

`a = 8√(2) cm`

Now, we can find the area of the square by squaring the side length:

Area =
`a^2`

Area =
`8√(2)`

Area =
`64*2`

Area = 8 unit sq

The area of the square with a diagonal of 16 cm is 8 unit sq.

The probable question may be:

Find the area of the figure whose diagonal is 16 , all 4 side are equal and all 4 angles are 90 degree