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    Question

    A right triangular pyramid XYZB is cut from cube as shown in figure. The side of cube is 16 cm. X. Y and Z are mid points of the edges of the cube. What is the total surface area (in cm2) of the pyramid?

    A 48[(√3) + 1] Correct Answer Incorrect Answer
    B 24[4 + (√3)] Correct Answer Incorrect Answer
    C 28[6 + (√3)] Correct Answer Incorrect Answer
    D 32[3 + (√3)] Correct Answer Incorrect Answer

    Solution

    XB = BY = 8 given that Xy2 = 82 + 82 = xy = 8√2 Xz = yz = 8√2 cm Bare area of pyramid (equilateral D0 Whore side is 8√2 = √3 / 4 × (side)2 = √3 / 4 × 8√2 = √3 / 4 × 64 × 2 = 32√3 cm2 ∠ P = 900 BP = 4√2 Height = 4√2 Bp2+py2 = By2(PGT Satisfy height for 3 part in 4√2 Area = 3 × ½ × 8√2 × 4√2 = 96 ISA = 96 + 32√3 cm2

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