Question

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.

Answer 1

Base perimeter = 4a = 40

a = 10cm

Total length of edges = 92 cm

Length of total laterals edge = 92 – 40 = 52

Length of one laterals edge = \(\frac{52}{4}\) = 13 cm

Slant height of lateral surfaces is l = \(\sqrt{13^{12} - 5^2}\)

= \(\sqrt{169-25}\)

= \(\sqrt{144}\)

= 12 cm

Surface area of pyramid = Base area + 2 x Perimeter of base x length of slant height of lateral surfaces

= a² + 1/2 pl

= 10² + 1/2 x 40 x 12

= 100 + 240

= 340 cm²

OR

Surface area of pyramid = a² + 2 al

= 10² + 2 × 10 × 12

= 100 + 240 

= 340 cm²