Q7 of 35 Page 197

What is the surface area of a square pyramid of base perimeter 64 centimetres and volume 1280 cubic centimetres?

Base perimeter is given as 64 cm.

So base edge


Volume is given as 1280 cm3.


We know that,





⇒ h = 15 cm


Let height of pyramid (h) = 15 cm


half of base edge = 8 cm


slant height = l


Applying Pythagoras theorem, we get:


l = √(152 + 82)


= √(225 + 64)


= √289


= 17 cm


Then area of one isosceles triangle



Area of four isosceles triangles = 4×136 = 544 cm2


Base area = 162 = 256 cm2.


Total surface area = (544 + 256) = 800 cm2


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