Question

Find the height of a rectangular prism if the surface area is 458.17in^2, the width is 6.2in and the length is 8.3in.

Answer 1

Find the surface area of all the sides with a width and length first can you do that?

Answer 2

? hello?

Answer 3

@Icedragon50 trying to figure out if i can lol

Answer 4

ok

Answer 5

@Icedragon50 just got one surface area, 8.3(6.2)=51.46

Answer 6

well heres a hint: two sides have an area of width * length

Answer 7

@Icedragon50 yeah i did that and got 51.46 lol

Answer 8

Very good!
now since theres TWO sides
so multiply by 2 to get:102.96

Answer 9

102.92 srry

Answer 10

@Icedragon50 aaah okay so what's next?

Answer 11

Ok so now we have 4 more faces.
2 of them are width*height and length*height

Answer 12

width*Height would be 6.2*h=6.2h

Answer 13

length*height would be 8.3*h=8.3h

Answer 14

now you solve for h (height) by using this equation:
102.92+6.2h+8.3h=458.17

Answer 15

@Icedragon50 h=24.5?

Answer 16

102.92+14.5h=458.17
14.5h=458.17-102.92
14.5h=355.25
h=24.5

So, height is 24.5

Answer 17

yes lol

Answer 18

@Icedragon50 that isn't any of my options :(

Answer 19

wit are your options??

Answer 20

@Icedragon50 10.25
12.25
14.25
16.25

Answer 21

:O

Answer 22

hmmm gimmee a sec

Answer 23

do you know what surface area is?

Answer 24

first, draw a rectangular prism and see if you can better visualize the problem

Answer 25

@nincompoop i did on my paper

Answer 26

draw it here

Answer 27

OK THIS TOOK ME FOREVER BUT HERE IT IS

Answer 28

SA = Surface Area = 458.17 in²
L = Length = 8.3 in
W = Width = 6.2 in
H = Height = What we're solving for.

The formula for the surface area of a rectangular prism is

SA = 2*(LW + LH + WH)

Substituting values:

458.17 = 2*(8.3*6.2 + 8.3H + 6.2H)

229.085 = 51.46 + 14.5H

14.5H = 229.085 - 51.46

H = 117.625/14.5

H = 12.25 inches.

That's about it! =)