# A right triangular pyramid XYZB is cut from the cube as shown in the f

| A right triangular pyramid XYZB is cut from the cube as shown in the figure. The side of cube is 16 cm. X, Y, and Z are midpoints of the edges of the cube. What is the total surface area (in cm

^{2}) of the pyramid?A. 48[(√3) + 1]

B. 24[4 +(√3)]

C. 28[6 + (√3)]

D. 32[3 + (√3)]

### Right Answer is: D

#### SOLUTION

Length of BX, BY & BZ = 8 cm

In triangle BXY:

BX = BY

Then BXY = BYX = 45^{o}

Hence XY = 8√2 cm

Similarly

XZ = YZ = 8√2 cm

Base of pyramid will be equilateral triangle,

T.S.A. of pyramid = C.S.A. of three right angle triangle + Base Area

= 96 + 32√3

= 32(3 +√3) cm^{2}

Share

A right triangular pyramid XYZB is cut from the cube as shown in the f