Question

If the length of the longest straight line that can be drawn in a square is 8 cm, what is the area covered by the square (in cm2)?

Answer 1

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Answer 2

Given:

The length of the longest straight line=8cm

To find:

The area that is covered by the square

Solution:

The area covered by the square is 32$cm^{2}$.

We can find the area by following the steps given below-

We know that the longest straight line that can be drawn in a square is the diagonal.

Let the side of the square be A.

The length of the longest straight line=The length of the diagonal of the square=8cm

The length of the diagonal of the square=$\sqrt{2}$A

Equating the values,

$\sqrt{2}$A=8

A=8/$\sqrt{2}$ cm

Now, we will calculate the area of the square.

The area covered by the square=$A^{2}$

Using the value of A, we get

=8/$\sqrt{2}$ ×8/$\sqrt{2}$

=64/2

=32$cm^{2}$

Therefore, the area covered by the square is 32$cm^{2}$.