Question

the percentage error in the side of square in 3% then calculate percentage error in its area​

Answer 1

It depends on how the area has then been calculated, and whether the incorrect measurement has stopped us thinking of it as a square.

Case 1: We think of it as a square, only took the one measurement, and used the "area of a square" formula, to calculate the area.

In this case, An undermeasurement of 3% means that we now think the square is only 0.97 times its real value.

We then calculate the area, and the error factor is 0.97 x 0.97 = 0.9409

1 - 0.9409 = 0.0591

So the error factor is 5.91%

Case 2: We measured two adjacent (not opposite) sides, and now think that the shape is actually a rectangle, so use the "area of a rectangle" formula.

In this case, an undermeasurement of 3% multiplied by a correct measurement gives us:

0.97 * 1 = 0.97

1 - 0.97 = 0.03

So the error factor is 3%

Case 3: We measured all four sides of the shape, and thought that we had something that was a rectangle plus a triangle.

In this case, see the nice picture in User's answer to Because of an error in measurement, the side of a square is measured 3% less than its actual length. What is the percentage error in the calculation of area?

The rectangle calcs work as in my case 2 above... but the triangle makes up half of the error...

So the error factor is 1.5%