Q4 of 35 Page 195

A square pyramid is to be made with the triangle shown here as a lateral face. What would be its height? What if the base edge is 40 centimetres instead of 30 centimetres?


LH = Height of pyramid


HG = Half of a diagonal


BC = base edge = 30cm


LG = lateral edge = 25cm


BG = Full diagonal = √(302+ 302) = 30√2 cm



By Pythagoras theorem


HL = √(LG2 + HG2)


= √(252 + (15√2)2)


= √(625 + 450)


= √1075 cm



LH = Height of pyramid


HG = Half of a diagonal


BC = base edge = 40cm


LG = lateral edge = 25cm


BG = Full diagonal = √(402+ 402) = 40√2 cm



By Pythagoras theorem


HL = √(LG2 + HG2)


= √(252 + (20√2)2)


= √(625 + 800)


= √1425 cm


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