How do I find surface area and slant height (do not include base) of a pyramid?

Question

height is 482ft

square base is 755ft

Answer 1

Use Pythagorean Theorem a² + b² = c²  to find slant height:

Since one side of base of pyramid is 755ft, divide by 2 = 377.5ft to get base of right triangle that formed by height and slant height of pyramid.

Let a = length of base of triangle

      b = length of height of triangle 

      c = length of slant height

     

(377.5)² + (482)² = (c)²

          374830.25 = c²

          612.2338 ft. ≈ c

 

Surface Area of pyramid: SA= B + 1/2(P)(l)    Where B =Area of base of pyramid

                                                                              P = perimeter of base of pyramid

                                                                                 l = slant height of pyramid   

                                          = 755² +1/2(755•4)(612.2338)

                                          = 570025 + 924473.0678 ≈ 1,494,498.068 ft²