XAT 2016 — QA & DI Question 10
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 unfolder original piece of paper?
Answer & solution
400 sq.cm.
- B
800 sq.cm.
- C
800√2 sq.cm.
- D
1600 sq.cm.
- E
Insufficient data to answer
When a square piece of paper is folded along its diagonal we will get a right isosceles triangle whose area becomes half.
Hence, after 3 such folds we get a right isosceles triangle, whose area is 1/8th the area of the original square.
Area of the folded triangle = ½ × 10 × 10 = 50.
∴ Area of the original square = 8 × 50 = 400 cm2.
Alternately,
If the side of the isosceles triangle is 10 cm then we get the side of the square as 20 cm on unfolding it.
Hence, the area of square = 400 cm2.
Hence, option (a).