Question

A sheet of paper square shape is folded into two equal parts so as to form the sea two overlapping rectangles. Knowing that the perimeter of the rectangle is 12 cm, what is the area of the original square?

A. 9 cm²
B. 36 cm²
C. 24 cm²
D. 72 cm²
E. 16 cm²

Answer 1

To find the area of the original square, the side of the square 's' is calculated using the given perimeter of the rectangle formed after folding, which is 12 cm. Solving 3s = 12 cm gives s = 4 cm, and hence the area of the square is 16 cm².

Step-by-step explanation:

The question asks us to find the area of the original square given that when it is folded into two equal parts, it forms a rectangle with a perimeter of 12 cm. Since the rectangle is made by folding the square, one side of the rectangle will be equal to the side of the square, and the other side will be half the length of that side. If we denote the side of the square as 's', then the rectangle will have one side 's' and another side 's/2'. The perimeter of the rectangle is given as 2(s + s/2) = 3s.

Setting the perimeter equal to 12 cm gives us 3s = 12 cm, so s = 4 cm. Therefore, the area of the square would be s² = 4 cm · 4 cm = 16 cm², which corresponds to option E.