Question

Find the surface area and volume of the square pyramid.

Picture below:

WILL GIVE MEDAL!!

Answer 1

ok so what is the formula for the volume of a square pyramid?

Answer 2

\[V=a ^{2}\frac{ h }{ 3 }\] right? @Brill

Answer 3

Yes, so now substitute in the correct numbers,
then you get
\[V=16^2\times \frac{ 24 }{ 3 }\]

Answer 4

thanks, and what about surface area? @Brill

Answer 5

So for surface area it is a bit more complicated.
The easiest first step is to find the area of the square at the bottom which is?

Answer 6

256? @Brill

Answer 7

Yep, just keep that number in mind

Answer 8

So now you need the area of the other 4 triangle sides
what you need to do involves the triangle with the dotted lines that they drew for you, do you see the on Im talking about?

Answer 9

i know what you are talking about, it's just this is the part I needed help on @Brill

Answer 10

Thats what you have, since the very top of the triangle is in the middle of the square couldn't you say that x is 1/2 the side of the square?

Answer 11

yes, and then what would you do?

Answer 12

So 1/2 of 16 is 8, do pythagorean theorem and you should get the height.

Answer 13

my problem is, what numbers would you plug in for which variable?

Answer 14

like which number for a, which for b, and which for c?

Answer 15

Well your height is the hypotenuse right? since it is across from the largest angle, so it is c, a and b can be used interchangeably with 24 and 8

Answer 16

by height I mean h

Answer 17

ok so, hold on a sec...

Answer 18

\[h ^{2}=24^{2}+8^{2}\]

Answer 19

Yes, now solve for h

Answer 20

would h be \[8\sqrt{10}\] ?

Answer 21

or did I do that wrong...

Answer 22

Yes so now you have the height you can take the area of 1 of the side triangles and multiply it by 4, then add it to the area of the base and you have your answer