Question

Find the value of p in the right triangular prism if the surface area is 457.25 in2
16.65 in
8.75 in
14.25 in
9.45 n

Answer 1

This one is a bit more involved. The surface area of the prism is the sum of the area of each side. We've got to find the hypotenuse of the triangle forming the end, call it h. Then the slanting face will have area p*h, the bottom face will have area 6.2*p, the back side will have area 9.9*p and the ends will each have area 1/2*6.2*9.9. Sharpen that pencil and get to work :-)

Answer 2

I got 11.68 for the hypotenuse

Answer 3

How will I write out this formula?

Answer 4

11.68 is correct for hypotenuse.

I pretty much wrote the formula for you. S = p*h + 6.2*p + 9.9*p + 2 * (1/2)*6.2*9.9, and you know what S equals from the problem statement.

Answer 5

what is h?

Answer 6

h was the value you found for the Hypotenuse

Answer 7

"We've got to find the hypotenuse of the triangle forming the end, call it h"

Answer 8

So am I divided the surface area with all the measurements I have in that formula?

Answer 9

dividing *

Answer 10

do you know what the area of a rectangle is?

Answer 11

30.69?

Answer 12

well, lemme give you one :/
what would be the area for the rectangle above?

Answer 13

kinda crooked but anyhow, length is 10, width is 8 :)

Answer 14

A = 8 * 10

Answer 15

right, so what you're doing with the prism is just adding all its faces, which are really just 3 rectangles and 2 triangles, and equate the SUM of all those AREAS to 457.52

Answer 16

area of a triangle is 1/2base times height, so you add that as well, and for the triangles there, you're given those 2 values, base = 6.2, and height = 9.9

Answer 17

now "p", you dunno, so you leave it as a variable, and you'd end up with an equation, which you solve for "p" :)

Answer 18

so one rectangle area will be
p times (11.68)

another rectangle will be
p times (9.9)

yet another rectangle will be
p times (6.2)

one triangle area will be
\(\cfrac{1}{2}\times 6.2 \times 9.9\)

another triangle area will be
\(\cfrac{1}{2}\times 6.2 \times 9.9\)

add them all up and they = 457.25

Answer 19

so, how would your equation look like?

Answer 20

457.25 in2 = 1/2 6.2 (9.9) + p * 11.68 + p * 9.9 + p * 6.2

Answer 21

you only forgot to add 1 triangle, so
$$
\color{red}{457.25} = \cfrac{1}{2}6.2 (9.9)+\cfrac{1}{2}6.2 (9.9) + p * 11.68 + p * 9.9 + p * 6.2
$$

Answer 22

now just add up the right-hand-side, then solve for "p"

Answer 23

I got 5.2 = p

Answer 24

5.2, well, if p = 5.2, take a peek at the picture, is P side really shorter than 6.2in side?

Answer 25

adding all the measurements on the right I got 89.16

Answer 26

hmm, what do the areas of the 2 triangles only, give you?

Answer 27

61.38

Answer 28

ok, what about the other rectangles, the "p" elements

Answer 29

27.78

Answer 30

27.78p, don't forget the variable
so, what you have is


457.25 = 61.38+27.78p

solve for "p"

Answer 31

p = 368.09?

Answer 32

well, take a peek at picture, does "p" look 61times bigger than the 6.2in side?

Answer 33

longer/bigger

Answer 34

hehe, I wonder where does numbers are coming from

Answer 35

just solve it for "p" and you'd know what "p" is :)