Please help finding the surface area of a composite figure

J

jhonmcgiver

New member
Joined
Nov 10, 2020
Messages
6
Assuming each cube has a side length of 1 unit.
What is the surface area of the solid figure?

Composite prism.PNG
 
How many squares on the left side that you can't see?
How many at the back that you can't see?
How many underneath that you can't see?
All the others you can see, and at the very least, you can count.
Give it a go! Then we can check your answer if you like.
 
Harry_the_cat said:
How many squares on the left side that you can't see?
How many at the back that you can't see?
How many underneath that you can't see?
All the others you can see, and at the very least, you can count.
Give it a go! Then we can check your answer if you like.
Click to expand...
I know the process, I just can't see to put all the pieces together

I know the volume is 120.

I know the individual area of each figure is
A1 = 8(2) = 16
A2 = 12(2)= 24
A3 = 6(2) = 12

B1 = 12(2) = 24
B2 = 16(2) = 32
B3 = 12)2) = 24

C1 = 12(2) = 24
C2 = 24(2) = 48
C3 = 12(2) = 24

I just don't know what to do next. Do I add all the numbers together? Do I need to substract the overlapping cubes? I have seen many videos and read many tutorials but all seem to side very simple shapes or formulas that don't work for this specific example.

If it was an easy as counting the cubes I can't see, I would not have posted a thread here.
 
jhonmcgiver said:
I know the process, I just can't see to put all the pieces together

I know the volume is 120.

I know the individual area of each figure is
A1 = 8(2) = 16
A2 = 12(2)= 24
A3 = 6(2) = 12

B1 = 12(2) = 24
B2 = 16(2) = 32
B3 = 12)2) = 24

C1 = 12(2) = 24
C2 = 24(2) = 48
C3 = 12(2) = 24

I just don't know what to do next. Do I add all the numbers together? Do I need to substract the overlapping cubes? I have seen many videos and read many tutorials but all seem to side very simple shapes or formulas that don't work for this specific example.

If it was an easy as counting the cubes I can't see, I would not have posted a thread here.
Click to expand...
Think about it! How do you calculate the total surface area of a cube?
You calculate the surface area of the front & the back & the top & the bottom & the left & the right sides of the solid​
and then add those all together. Same principle here.​

First - you need to define your assumed variables:

What is A1? Where are you getting the number 8?

Let us define the "rectangular" area on which the object is sitting (bottom) as S1. According to my vision:

S1 = 7 * 4 = 28 ................................... do you see that?​

Let us define the area on the left side of the object (invisible to perspective) as SL. According to my imagination:

SL = 6 * 4 = 24​
​
Now continue........

1605007927692.png
 
30 on the front, 30 on the back
12 on the right, 24 on the left
28 on the bottom, 40 on the top.
Adding it all up, it should be164.

Is this the right surface area?
 
Subhotosh Khan said:
Incorrect.

You say:
30 on the front, 30 on the back

How did you get that?
Click to expand...
I counted 30 on the front, and because I know the back must be the same number, I just added another 30.

is the same 88+80+52 = 20?

I separated the figure into 3 rectangular prims and added the surface area of each.
 
Harry_the_cat said:
I agree with that calculation. Assuming that the figure is solid.
Click to expand...
1605057119849.png The bottom (invisible) rectangular face has 7* 4 cubes → surface area = 28

Back rectangular face (invisible) has 6 * 4 cubes → surface area = 24

Stepped area → 4 * 3 + 4*2+ 4 * 1 + 4*3 + 4 * 2 + 4*2 → surface area = 52

Front and back L shaped area → 2*(7 * 3 +5*1 + 2*2) = 60

Total surface area = 28 + 24 + 52 + 60 = 164

That is the complete work - and you should explain your work step-by-step.
 
Subhotosh Khan said:
View attachment 23036 The bottom (invisible) rectangular face has 7* 4 cubes → surface area = 28

Back rectangular face (invisible) has 6 * 4 cubes → surface area = 24

Stepped area → 4 * 3 + 4*2+ 4 * 1 + 4*3 + 4 * 2 + 4*2 → surface area = 52

Front and back L shaped area → 2*(7 * 3 +5*1 + 2*2) = 60

Total surface area = 28 + 24 + 52 + 60 = 164

That is the complete work - and you should explain your work step-by-step.
Click to expand...

This is just a minor misunderstanding.

Your 6*4 face is define as "back" while I am defining it as "left"
Your stepped area is a combination of my Top face = 40, and left face =12 so together they make your stepped area's 52
I am diving it between just the top faces 40 and the left face 12.
our bottom is the same.

We dived the polygon into different parts but we both had the same answer.
Telling me that my response was incorrect even though we had the same answer
because I didn't follow your exact method was the wrong thing to do.
The beauty of math is that we can all arrive at the same answer using a variety of different approaches.

Regardless, I wanted to thank you for your patience and help. I was confused and dialoging with you helped me organize my thoughts.
I wish you a good day.
 
You must log in or register to reply here.
Top