Q1 of 35 Page 195

Using a square and four triangles with dimensions as specified in the picture, a pyramid is made.


What is the height of this pyramid?


What if the square and triangles are like this?


From the first figure we get.


Slant Height LG = 18cm


Base BC = 24cm


Height of pyramid



= √ (324 – 122)


= √ (324 – 144)


Height AC = √180 cm = 6√5 cm


From the second diagram we get,



LH = Height of pyramid


HG = Half of a diagonal


BC = base edge = 24cm


LG = lateral edge = 30cm


BG = Full diagonal = √(242+ 242) = 24√2 cm



By Pythagoras theorem


HL = √(LG2 – HG2)


= √(302 – (12√2)2)


= √(900 – 288)


= √612 cm


More from this chapter

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4

The perimeter of the base of square pyramid is 40 centimetres and the total length of all its edges is 92 centimetres. Calculate its surface area.

 5

Can we make a square pyramid with the lateral surface area equal to the base area?

 2

A square pyramid of base edge 10 centimetres and height 12 centimetres is to be made of paper. What should be the dimension of the triangles?

 3

Prove that in any square pyramid, the squares of the height, slant height and lateral edge are in arithmetic sequence.