Question

please help

Answer 1

What is the surface area of this three-dimensional, symmetrical, capital letter “I” block? Show your work.

Answer 2

i know how to do the fir

Answer 3

i just don't know how to subtract the interior faces

Answer 4

I would count the number of exterior faces.

Answer 5

this is what i have so far:
there are 3 rectangular prisms. the prisms are 2 cm tall and 5 cm wide.
SA= 2lw+2lh+2wh
SA= 2x2x5 + 2x2x2 + 2x2x5
SA= 20 + 8 + 20
SA= 48
Now you have to do 48x3 because there are three rectangular prisms
48 x 3= 144
The surface area of the shape is 144

Answer 6

or at least the area of each region.

Answer 7

i know the surface area but i dont know what to do for the enterior faces

Answer 8

For example, the "front" of the "I" has 3 parts, the top has area 2x5=10 (and so does the bottom). the middle part is 2 high and 1 across = 2
total area of the front face is 10+10+2 = 22
we can assume the "back" face is also 22

Answer 9

the top of the I is also 5 x 2. The bottom of the I (which we can't see) is 5 x 2
top and bottom are 10+10=20

so front + back + top + bottom = 42

Answer 10

now we need the area of the complicated "sides" which (because of the indent) has 5 faces

Answer 11

they all seem to be 2 x 2 = area 4
so 5* 4= 20
for the left side. the right side is the same, also 20
so that is another 40 to be added to the 42

82 total

Answer 12

i did this problem completely wrong didn't i

Answer 13

you had a good idea, but it did not work. That happens a lot in the "real world"
If that happens, you "go back to the drawing board", and try to think of another strategy.

Answer 14

though I added wrong.
front + back = 22+22= 44 (not 42)
front + back + top + bottom= 22+22+10+10= 64

the sides are 20 each, or 40 for left and right.
total area is 104

Answer 15

Your idea is actually good. we just have to tweak it.

the top and bottom prism are the same size and have a total surface area of 48 (as you found)

together the area is 48+48= 96

but a small part of the area is hidden by the middle section
the middle section has a "top" area of 2x1= 2 which is hidden
also has a hidden bottom area of 2x1= 2
that means we should subtract 2+2= 4 from the 96
96-4= 92

next, we add the surface area of the middle part. 2 sides are 1x2 and 2 sides are 2x2
2*1*2 + 2*2*2= 4+8=12
add 12 to the 92:

12+92= 104

it matches!