Question

Find the lateral area the regular pyramid.
Need help to solve it

Answer 1

would you say that's about right for the BOTTOM of the hexagonal pyramid?

Answer 2

5 times 6 times 6

Answer 3

180?

Answer 4

yes

Answer 5

ok, so, what would be "green" line? using the pythagorean theorem

Answer 6

5
so the answer is 180

Answer 7

would i set it up as 6^2 + 6^2 = x ?

Answer 8

well,
$$
c^2= a^2+b^2\\
\text{what you need is "b",solve for "b"}\\
b^2 = c^2-a^2 \implies b = \sqrt{c^2-a^2}
$$

Answer 9

from the right-angle, you have the hypotenuse, or "c", which the longest side, 6
the adjacent, or the shorter given side, or "a" which is 3

Answer 10

ok so b^2 = sqrt7 ?

Answer 11

yes

Answer 12

or \(\sqrt{27} = 3\sqrt{3}\)

Answer 13

so, now let's find the lateral sides "nose", or the so-called "slant-height"

Answer 14

keep in mind that, though slanted for perspective, the "yellow" triangle is a right-triangle
so, using the known values, 8 and \(3\sqrt{3}\), use the pythagorean theorem to get the "longest" side, the one going to the top of the pyramid

Answer 15

the "longest" side will be the hypotenuse
the opposite side, that is "b" is 8
the adjacent side, that is "a" is \(3\sqrt{3}
$$
c^2= a^2+b^2\\
3\sqrt{3} = \color{blue}{\sqrt{27}}\\
c^2 = (\color{blue}{\sqrt{27}})^2+(8)^2\\
c = \sqrt{(\color{blue}{\sqrt{27}})^2+(8)^2}\\
$$

Answer 16

hmmm

Answer 17

hehe my bad :)

Answer 18

the "longest" side will be the hypotenuse
the opposite side, that is "b" is 8
the adjacent side, that is "a" is \(3\sqrt{3}\)
$$
c^2= a^2+b^2\\
3\sqrt{3} = \color{blue}{\sqrt{27}}\\
c^2 = (\color{blue}{\sqrt{27}})^2+(8)^2\\
c = \sqrt{(\color{blue}{\sqrt{27}})^2+(8)^2}\\
$$

Answer 19

c= 729 + 64 which = 793. So i then squareroot 793 ?

Answer 20

well, \((\sqrt{NUMBER})^2 = NUMBER\)

Answer 21

so
\(c = \sqrt{(\color{blue}{\sqrt{27}})^2+(8)^2} = \sqrt{27+64} = \sqrt{91}\)

Answer 22

so, now you just need to find the area of that triangle, that one face

area of a triangle = \(\large \cfrac{1}{2} \times base \times height\)

you get that area, the pyramid is a hexagon, so there are 6 of those triangles, add them together, and that's your Pyramid Lateral Area

Answer 23

180/2=90 which is final answer

Answer 24

base= 6 and height= sqrt 91 right?

Answer 25

yes

Answer 26

the area is sqrt 273?

Answer 27

$$
\cfrac{1}{2}\times 6 \times \sqrt{91} = 28.6\\
28.6\times 6 = 171.6
$$

Answer 28

so i add all 6 and get 1,029.6

Answer 29

ahemm well, 1 triangle, that is 1 side, 1 lateral, is 28.6 in Area
so 28.6 + 28.6 + 28.6 + 28.6 + 28.6 + 28.6 = 171.6

Answer 30

Oh. so the lateral area is 171.6?

Answer 31

yes, for a pyramid, the "laterals" or the "sides" area, that is, not including its bottom/base
is the area of all her triangles around her

Answer 32

this one is a HEXAgon, so 6 sides, so 6 triangles, so you add them up

Answer 33

Thank you so much!!!

Answer 34

yw