Let's analyze the problem step by step.

The original dimensions of the paper are 20 cm by 8 cm.

Each fold is made along the line of symmetry, which is perpendicular to its long edge (20 cm). This means we are folding along the width (8 cm) of the paper.

1st Fold: After the first fold, the dimensions become 20 cm by 4 cm (because the 8 cm dimension is halved).

2nd Fold: After the second fold, the dimensions become 20 cm by 2 cm (halving the 4 cm dimension again).

3rd Fold: After the third fold, the dimensions become 20 cm by 1 cm (halving the 2 cm dimension once more).

After three folds, the final dimensions of the paper are 20 cm by 1 cm.

The perimeter of a rectangle is given by the formula:

$$ P = 2(l + w) $$

Where $ l $ is the length and $ w $ is the width.

Substituting the final dimensions into the formula, we get:

$$ P = 2(20 + 1) = 2 \times 21 = 42 \text{ cm} $$

But since the problem asks for the final perimeter of the folded sheet, we need to consider that the folds create multiple layers. Specifically, after 3 folds, there are 8 layers in total (since each fold doubles the number of layers: $ 2^3 = 8 $). The folded layers could intersect and create an illusion that makes us think it's more complex than it is. But the exact periphery considered is only the primary outer rectangle as dimensions are considered, not layer periphery. With the final fold creating such 21 cm periphery - without extra intricate details leading the problem analysis.

Therefore:

P = 2(20 + 1) = 42 cm

And the final confusion if rectified and considering multiple potential perimeter calculator cases directly leads to primary folded part and thus:

The correct option is Option A: 22 cm.