A circle is inscribed in an equilateral triangle of side 24 cm, touching its sides. What is the area of
the remaining portion of the triangle?
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Points P, Q, R and S are taken on sides AB, BC, CD and DA of square ABCD respectively, so that AP : PB = BQ : QC = CR : RD = DS : SA = 1 : n . Then the ratio of the area of PQRS to the area of ABCD is
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Three cubes with integer edge lengths are given. It is known that the sum of their surface areas is 564 cm2 Then the possible values of the sum of their volumes are
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A solid metallic cube is melted to form five solid cubes whose volumes are in the ratio 1 : 1 : 8: 27: 27. The percentage by which the sum of the surface areas of these five cubes exceeds the surface area of the original cube is nearest to:
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Let ABCDEF be a regular hexagon with each side of length 1 cm. The area (in sq cm) of a square with AC as one side is
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