The slant height of a square pyramid is 25 centimetres and its surface area is 896 square centimetres. What is its volume?

Let the base edge be (2a) cm

Then area of one isosceles triangle

.

Area of four isosceles triangles = 4×25a = 100a cm².

Base area = (2a)² = 4a² cm².

Total surface area = (100a + 4a²)cm²

Given total surface area = 896

∴ 100a + 4a² = 896

⇒ a² + 25a – 224 = 0

Using,

We get,

⇒ a = 7 or – 32

Since, base edge cannot be negative

∴ a = 7 cm

LG = Slant height = 25cm

HG = Half of base = 7cm

Apply Pythagoras theorem

LH = √(25² – 7²)

= √(625 – 49)

= √576 = 24cm

Volume of a pyramid

Volume of a pyramid