Question

How do I find the total area of this prism?

Answer 1

@acxbox22 @mathslover can either of you help me with this question?

Answer 2

you want the area of the prism or volume?

Answer 3

The area

Answer 4

surface area or lateral surface area?

Answer 5

Lateral area first then the total area

Answer 6

The formula for LA is perimeter x height

Answer 7

yeah, so first of all use the pythagorean theorum to find the hypotenuse of the triangle base
then we cand find perimeter

Answer 8

\[4^{2} + 6^{2} = x ^{2}\]

Answer 9

can you find out the 3rd side side yourself?

Answer 10

so 16 + 36 = 52 and the \[\sqrt{52} = 2\sqrt{13}\]

Answer 11

do I add that to the area of the 3 rectangles?

Answer 12

no because we need perimeter\[6+4+2\sqrt{13}=10+2\sqrt{13}\]

Answer 13

So that would be the perimeter?

Answer 14

Then I multiply that by the height (8)?

Answer 15

yes, to get lateral surface area

Answer 16

So the LA = \[80 + 16\sqrt{13}\]

Answer 17

yes good job

Answer 18

Thank you!!! So from there, how do I find the total area?

Answer 19

Total Area = LA + 2B

Answer 20

It should be logical to think that there are h (height) number of triangles (the triangles of the surface top) .

Answer 21

total surface area
just add the area of the 2 bases to the lateral surface area

Answer 22

So the area of the 2 bases would be the same as the area of the triangle before right? \[2 \sqrt{13}\]

Answer 23

2[(6 x 4)/2]+80+16sqrt13

Answer 24

no 2sqrt13 was the perimeter not the area

Answer 25

That would make the h = 8 right? @SolomonZelman

Answer 26

Oh ok I will work that out

Answer 27

\[104 + 16\sqrt{13}\]

Answer 28

@acxbox22 is that right for the TA?

Answer 29

Yes there are many right triangles with legs 4 and 6 (that means that the height and base are these legs). Find the area of this (top surface) triangle, and multiply times height (which is 8).

Answer 30

@SolomonZelman that would = 96 correct? Which part is this for--total area?

Answer 31

yes you are correct.

Answer 32

\(\normalsize\color{blue}{ ' }\) probably means feet, so just say \(\normalsize\color{blue}{ 96 ft.^{2} }\)

Answer 33

and yes @rcschooool you are correct for both parts
good job

Answer 34

@SolomonZelman 96ft^2 is the volume not the surface area

Answer 35

oh, was the question surface area?
Then find the area of each different surface add them together and multiply by 2. You should have 6 surfaces overall.

Answer 36

Thank you!

Answer 37

@acxbox22 i have one more total area question, could you explain how to do this one?

Answer 38

sure

Answer 39

Thank you!!

Answer 40

It gives me the perimeter as 20 already

Answer 41

so do you need lateral surface area or total surface area?

Answer 42

Total area, but do i need to find the lateral area first in order to find the total area?

Answer 43

Lateral area = 120 right? (I multiplied 20 (perimeter) by 6 (height) @acxbox22

Answer 44

yes that is the lateral surface area
now we need to find the area of the 2 pentagons to find the total surface area

Answer 45

what does that say on the line on the pentagon?

Answer 46

It says K. I need to find the total area in terms of "k"

Answer 47

oh... http://formulas.tutorvista.com/math/area-of-a-pentagon-formula.html

Answer 48

so it will be 120+(the area of the 2 pentagons in terms of k)

Answer 49

so \[\frac{ 5 }{ 2 } \times 4 \times k\]

Answer 50

which equals 10k for the area of one pentagon

Answer 51

so I would just multiply that by 2? 20k = area of both of the pentagons?

Answer 52

yes, i am pretty sure that is correct

Answer 53

so the TA would be 120 + 20k. thanks for your help!

Answer 54

;)