Question

A square has a diagonal with length 12.2. what is the area of the square to the nearest tenth?

Answer 1

The diagonal of a square is related to the length of the side of the square by
$d=\sqrt 2 L$
where d is the diagonal, and L the length of the side. We are told the diagonal of this square, d=12.2, so we can find the length of the side by rearranging the previous equation:
$L= \frac{d}{ \sqrt{2} } = \frac{12.2}{ \sqrt{2} } =8.6$

and now we can calculate the area of the square, which is given by the square of the length of the side:
$A=L^2=(8.6)^2=74.0$

Answer 2

Answer:

Area of the square is 74.4 unit².

Step-by-step explanation:

A square has a diagonal with length 12.2 units.

We have to find the area of the square.

Since all angles of a square are of 90° so by Pythagoras theorem

Side² + side² = Diagonal²

Let the length of the diagonal is d and length of sides be l.

l² + l² = d²

2l² = d²

$l^{2}=\frac{d^{2} }{2}=\frac{(12.2)^{2} }{2}$

Since area of a square = side² = l²

Therefore area of square = $\frac{12.2^{2} }{2}=\frac{148.84}{2}=74.42unit^{2}$

Area of the square is 74.4 unit².