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. $$48\left[ {\left( {\sqrt 3 } \right) + 1} \right]$$

B. $$24\left[ {4 + \left( {\sqrt 3 } \right)} \right]$$

C. $$28\left[ {6 + \left( {\sqrt 3 } \right)} \right]$$

D. $$32\left[ {3 + \left( {\sqrt 3 } \right)} \right]$$

Answer: Option D

Solution (By Examveda Team)

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