Pyramid- prism?

Question

Khafre Pyramid in Egypt – a square pyramid Base measurements
Side = 215 m
Height=145 m

Aon Center, Chicago – a rectangular prism (square base)
Base measurements Side = 40 m
Height=345 m
find the surface area and volume of a prism and a pyramid and also the slant height of the pyramid base area from both
I have this results from the pyramid please correct me showing the work thank you'
this what I have :
dimensions of the base 860 m slant height259.326 base area46225 m^2 lateral area 111510.18 m^2 surface area 157735.18 m^2 volume 20783 m^3
I am a little lost with the prism

Answer 1

For the pyramid, if you mean a side of the square base is 215 m, then your slant height is wrong. The slant height would be the hypotenuse of a right triangle with the vertex of the right angle in the center of the base of the pyramid, one leg equal to the height (145) and one leg equal to half the side of the base (107.5). So by Pythagorean Theorem, slant height = sqrt(145^2 + 107.5^2), or about 180.5 m. That will in turn throw off your lateral area.

The volume is 1/3 times area of base (which you have correct) times height. I did not get 20783 when I did that.

As for the prism, it's just a box like shape. Its volume is area of base times height. That's 40(40)(345)

Surface area is the sum of the areas of each surface, which are rectangles. Four of them (the lateral faces) are 40 by 345, and the top and bottom are squares (40 by 40)

Hope that helps!