Question

Help!!
Find the Lateral Area!
(__+__sqrt__)

https://media.glynlyon.com/o_geo_2010/8/groupi68.gif

Answer 1

the area of which side?

Answer 2

sorry i meant face not side (i'm not sure what is the proper term in english)

Answer 3

Of the whole prism

Answer 4

ok. did you notice that the top and the base are rectangle triangles??

Answer 5

The lateral area is the sum of the areas of the rectangles that form the faces (other than the bases) of the prism.

Answer 6

thank you!

Answer 7

You can do two of the rectangles easily: you know their width and length

Answer 8

the 3rd one is harder. You can use pythagoras to find the 3rd side of the triangle, which is the width of the 3rd face

Answer 9

Can you find the areas of the 2 easy faces?

Answer 10

I know that the sum of all three squares/rectangles is 104 and the c side is 7.21

Answer 11

how?

Answer 12

Well the "unknown" sides are squares. and squares are equal on all four sides soooo. you get the area of the rectangle which is 8*4=32 and 6*6= 36 and 6*6=36. and then when you do pythagorean theorem on the triangle, the long side is 7.21.

Answer 13

Oh and 32+36+36= 104

Answer 14

but the are for the triangle is 16. sooo 16+16= 32 and then 104+32= 136

Answer 15

area*

Answer 16

they want the answer in the form (__+__sqrt__)

so you are on the right track:
8*4 = 32 for one of the faces looks good
but the other face is not 6x6 (it is 6 wide and 8 high)

for the 3rd side of the triangle, do not change to a decimal
a^2+b^2 = c^2
4^2 +6^2 = c^2
16+36= c^2
52= c^2
c= sqrt(52)
you can simplify by factoring 52 into 4*13
c= sqrt(4)*sqrt(13) or
c= 2*sqrt(13)

now you can find the third face:
8 (the height)* 2*sqrt(13)= 16*sqrt(13)

add all three

Answer 17

and remember lateral area does not include the 2 bases (the triangles)

Answer 18

but 128 doesn't fit into the answer.

Answer 19

so im left with (__+16sqrt13)

Answer 20

the area of the 3 sides are: 32, 48, 16sqrt(13)
or
80+16*sqrt(13)

Answer 21

Ohh okay, I added the 3 rectangles
Thank you very much for helping!

Answer 22

Those are the 3 rectangles. Do you mean the two triangles (top and bottom)?
top and bottom add up to 24, so the surface area of the entire prism would be 24+80+16sqrt(13)= 104+16sqrt(13)
no 128 in sight anywhere!

Answer 23

but the lateral area is just the 3 rectangular sides: 4x8, 6x8, and 2sqrt(13) x 8
which add up to 80+16sqrt(13)

Answer 24

Long day. and yes if you add 48+48+32.

Answer 25

I need a break for the day!

Answer 26

I don't see how you got the 2nd 48. Hope it makes sense...

Answer 27

It makes a lotttt more sense now!