There are 9 squares I can see 12 squares in an array of 2 * 4 squares
Rectangular Prism
Eight squares are needed.
12 squares in total.
The rectangle can be thought of as two adjacent 12 x 12 squares. Each square has an area of 144 sq. ft., making the entire rectangle 288 sq. ft. thereby creating a needless extra step, since the area of the rectangle is 12 x 24 = 288 sq. ft.
There are 9 squares I can see 12 squares in an array of 2 * 4 squares
Well, A square is a type of rectangle, so I image 12 squares is the same as saying 12 rectangles. Unless the squares are touching each other, then if two squares are touching then another rectangle would be formed.. etc etc
Rectangular Prism
Use squares and try it out for yourself. Get a number of squares and make a rectangle 3 squares long by 4 squares wide. Count the squares. You should have 12 squares (or 3*4). That's the best way I know to prove the formula.
Eight squares are needed.
12 squares in total.
The rectangle can be thought of as two adjacent 12 x 12 squares. Each square has an area of 144 sq. ft., making the entire rectangle 288 sq. ft. thereby creating a needless extra step, since the area of the rectangle is 12 x 24 = 288 sq. ft.
That depends on the size of the suares. For example, there will be a million squares with sides of 0.001 ft each. If the 12 square ft area is in the form of a 6*2 rectangle, there will be space for 3 squares of 2*2. But if the area is 3*4 then 2*2 squares cannot cover it without overlap.
I think you are thinking of using the rectangles like you use Punnet squares. One side is multiplied times the other side and the product is put in the inside squares. This is handy when trying to factor expressions that are polynomials.
If for example the rectangles was 4 inches by 3 inches then by marking out 12 equal one inch squares within the rectangle you'll prove that 4 times 3 = 12 square inches.
The equation for a rectangle is h(height) x w(width) = area . By manipulating the equation we can show that width=area/length. So 132/12=11. This means the width of the rectangle is 11.
12 squares.