The vertices of square pyramid are A(0, 0, 0), B(4, 0, 0), C(4, 0, 4), D(0, 0, 4) and E(2, 6, 6)
(i) Volume of the pyramid is
Text Solution
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(i) Volume of pyramid = 
× base area × height = 
× 16 × 6 = 32
(ii) Co-ordinates of centroid of faces EAB, EBC, ECD & EDA are (2, 2, 2) 
, 
, 
. y-co-ordinate of each point is 2. hence these points are co-planar & plane is parallel to base plane.
(iii) ortho-centre of Δ ABD is (0, 0, 0) equation of plane EBC is 
= 0
4.((x – 4).6 + 2y) = 0 ⇒ 6x – 24 + 2y = 0 ⇒ 3x + y – 12 = 0
d = 
= 
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