Mohan was playing with a square cardboard of side 2 metres. While playing, he sliced off the corners of the cardboard in such a manner that a figure having all its sides equal was generated. The area of this eight sided figure is:
Explanation:
Refer to the following figure.
As all the sides of the figure are equal,
2 - 2x = x2
∴ x = 21+2 = 2 - 2 ...(rationalising the denominator)
Area of the eight sided figure = Area of the square – 4 × Area of each small triangle
= 2 × 2 - 4 × 12(2 - 2)2
= 4 - 2(6 - 42)
= 8(2 - 1)
= 82+1 ...(multiplying and dividing by (2 + 1)
Hence, option (d).
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