Question

5. Find the slant height of the square pyramid illustrated below that has a
surface area of 896 ft?. Round your final answer to the nearest foot.
(3 marks)
16 ft
16 ft

Answer 1

Answer:

  20 ft

Step-by-step explanation:

The formula for the surface area of a pyramid is often written in terms of the base dimensions and the slant height. We can solve that formula for the slant height.

  SA = base area + lateral area

  SA = b² + 2bs . . . . . where b is the base dimension, and s is the slant height

  SA -b² = 2bs . . . . . subtract the base area

  s = (SA -b²)/(2b) . . . . divide by the coefficient of s

Using the given values for surface area and base length, we find ...

  s = (896 -16²)/(2·16) = 640/32 = 20 . . . feet

The slant height of the pyramid is 20 feet.