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Question 64
A square piece of paper is folded three times along its diagonal to get an isosceles triangle whose equal sides are 10 cm. What is the area of the unfolded original piece of paper?
Solution
When a square sheet is folded in half, its area is also halved. Now, an isosceles right triangle is formed after folded. For 2nd & 3rd folds, again areas halved each time and isosceles right triangle is formed
Equal sides = 10 cm
Area of last such triangle = $$\frac{1}{2} \times 10 \times 10 = 50 cm^2$$
$$\therefore$$ Area of original square = $$50 \times 2 \times 2 \times 2$$
= $$400 cm^2$$
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