Question

Write a simplified expression that represents the...

a. area of the large rectangle.
b. area of the small rectangle.
c. area of shaded region.

Answer 1

See below

Explanation:

a.

• Area of the large rectangle = (6 + x) (6 - x)

• ->Area of the large rectangle
  `=(6)^2-x^2`

• -> Area of the large rectangle
  `= 36-x^2`

b.

• Area of the small rectangle = (2 + x) (2 - x)

• ->Area of the small rectangle
  `=(2)^2-x^2`

• ->Area of the large rectangle
  `= 4-x^2`

c.

• Area of shaded region = Area of the large rectangle - Area of the small rectangle

• -> Area of shaded region
  `=( 36-x^2)-(4-x^2)`

• -> Area of shaded region =
  `=36-x^2-4+x^2`

• -> Area of shaded region
  `=32 \:units^2`