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?

Answer: Option D

BX = BY = 8 cm
∴ XY = YZ = XZ = 8√2

$$l$$² = 8² - (4√2)²
$$l$$² = 32
$$l$$ = 4√2
Total surface area = $$\frac{1}{2}$$ × Perimeter of base × $$l$$ + Area of base
= $$\frac{1}{2}\times 3\times 8\sqrt{2}\times 4\sqrt{2}+\frac{\sqrt{3}}{4}{\left(8\sqrt{2}\right)}^2$$
= 96 + 32√3
= 32(3 + √3) cm²