Explanation:
oh, come on ! we are dealing with rectangles.
and you know how to get the perimeter and the area of a rectangle. upper elementary school students can do that.
remember, the perimeter is the distance when you walk all around the rectangle.
so, 2 times the length and 2 times the width.
and the area is simply length × width.
but your teacher was very lazy and careless with some phrasing about what is needed.
the original room is 8 ft × 3 ft.
1.
the length of border needed is exactly the perimeter.
so,
2×8 + 2×3 = 16 + 6 = 22 ft
2.
the area of the floor is
8×3 = 24 ft²
this is the amount of floor panels to be bought. we buy them in ft².
3.
the new room is (8+3) ft × (3-2) ft. = 11 ft × 1 ft.
that is a very strange room. no human can live in such a room.
I think your teacher meant (8-2) ft × (3+3) ft = 6 ft × 6 ft.
but let's stick with the original information.
the border for this room (perimeter) is
2×11 + 2×1 = 22 + 2 = 24 ft
4.
the floor area is
11 × 1 = 11 ft²
if we consider my correction of the room size, it is
6×6 = 36 ft²
5.
"difference in size" is not clear. regarding the dimensions (side lengths and correspondingly the perimeter) or regarding the floor size ?
if we consider the perimeter, the difference is
24 - 22 = 2 ft
the new room's perimeter is 2 ft less.
if we consider the floor area, the difference is
24 - 11 = 13 ft²
the new room is 13 ft² smaller.
or for my size correction, the difference is
36 - 24 = 12 ft²
the new room is then 12 ft² larger.