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

the Pyramid:
The slant height is 180.5 m.
(145)^2 + (215/2)^2 = c^2 (c is slant height)
it's a little more clear if you draw a picture... You get a right triangle: one leg is from the middle of the base to one side, the other leg is the height. The slant height would be the hypotenuse.

So, the surface area is
4* 1/2 * 215 * 180.5 + (215)^2
123840 sq meters
(The area of four triangle with slant height as the height and one side of the base as the base. Plus the area of the square base.)

The volume is
(1/3) * (145) * (215)^2
2234208.33 cubic meters
(Formula for a pyramid is 1/3 * height * area of base)

---------------
A rectangular prism is just a box.

There is no slant height. (it's the same as the regular height.)

Surface Area:
4*40*345 + 2*40*40 = 58400 sq m
(4 rectangles with dimentions 40x345, two squares with dimensions 40x40.)

Volume:
40 * 40 * 345 = 552000 cubic m
(volume of a box is length * width * height)

Answer 2

There appear to be two different pyramids described here.

Pyramid 1
Khafre Pyramid in Egypt – a square pyramid Base measurements
Side = 215 m
Height=145 m
To solve the area I initially determine the coordinates of 6 points including the mid point of one of the bases
I do not seem to be able to format an array so I will describe the following. it consists of 6 rows and 3 columns
x y z
A base x=0.0 y=0.0 z=0.0
B basex=215.0 y=0.0 z=0.0
C basex=215.0 y=215.0 z=0.0
D basex =0.0 y=215.0 z=0.0
E peakx=107.5 y=107.5 z=145.0
midABx=107.5 y=0.0 z=0.0
The area of the square base is 215*215=46225
The distance from midAB to "E peak" is
sqrt((107.5-107.5)^2+(107.5-0)^2+(145-0)^2)=180.50
The area of each of the 4 sides is the distance from the base to the peak times the length of the base.
=180.5*215/2=38808.1
The total area is 4 * 38808.1 + 46225=201457.4
The volume is 1/3 * the height times the area of the base
1/3*145*46225=184,000.00

Pyramid 2
Aon Center, Chicago – a rectangular prism (square base)
Base measurements Side = 40 m
Height=345 m
x y z
A x=0.0 y=0.0 z=0.0
B x=40.0 y=0.0 z=0.0
C x=40.0 y=40.0 z=0.0
D x=0.0 y=40.0 z=0.0
E x=20.0 y=20.0 z=345.0
midAB x=20.0 y=0.0 z=0.0
The area of the square base is 1600.0
The distance from midAB to "E peak" is 345.58
The area of each of the 4 sides is 13823.2
The total area is 56892.7
The volume is 184,000.00

Answer 3

in case you pick to locate the quantity of both together (that is what i imagine you recommend through the completed ingredient), enable's commence through looking the quantity of the sq. prism: 8 * 8 * 8 = 512 instruments^3. Now for the different section. the quantity of a pyramid with a oblong base is given through the formulation V = a million/3 * Length_of_base * width_of_base * height = a million/3 * 8 * 8 * 8 = about one hundred seventy.sixty seven instruments^3. together, the sum of both volumes may be 512 + one hundred seventy.sixty seven = 682.sixty seven instruments^3.