Question

In terms of x, find an expression that represents the area of the shaded region. The outer square has side lengths of x + 5 and the inner square has side lengths of x - 2.

Area: square units

Answer 1

14x +21 square units

Explanation:

If we assume that the inner square is wholly contained within the outer square, and that the shaded area is between the squares, then the shaded area is the difference of the square areas:

shaded area = (outer square area) - (inner square area)

= (x +5)^2 -(x -2)^2

= (x +5 +x -2)(x +5 -x +2) . . . . factoring of difference of squares

= (2x +3)(7)

= 14x +21

The shaded area is 14x+21 square units.