Q4 of 35 Page 193

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.

Let b be the base edge

And l be the lateral edge


Then we can write:


4b + 4l = 92 cm …..(1)


But 4b = 40 cm.


So we get


Substituting this value of b in (1) we get:


40 + 4l = 92


⇒ 4l = 52


⇒ l = 13cm


Altitude of one isosceles triangle = √(132 – 52)


= √(169 – 25)


= √144 = 12cm


Now, we can calculate the total surface area


Base area = 10 × 10 = 100cm2


Area of one isosceles triangle



Area of one isosceles triangle = 60cm2


Area of 4 isosceles triangle = 4 × 60 = 240cm2


Total surface area = 100 + 240 = 340cm2


More from this chapter

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