Question

What is the area of this face ?

Answer 1

Answer: The area of the face is 15 sq. in.

Step-by-step explanation:  We are given to find the area of the yellow-coloured face in the figure.

The area of the coloured face is equal to the area of one face of a cube of side 4 in MINUS the area of one face of a cube of side 1 inch.

The area of one face of a cube of side 4 in is given by

$A=\textup{area of a square of side length 4 in.}=4\times 4=16\textup{ sq. in.}$

and the area one face of a cube of side 1 in is given by

$a=\textup{area of a square of side length 1 in.}=1\times 1=1\textup{ sq. in.}$

Therefore, the area of the coloured face will be

$Area=A-a=16-1=15\textup{ sq. in.}$

Thus, the area of the face is 15 sq. in.

Answer 2

4•4 -1•1 = 16-1 = 15 square inches