Question

PLEASE HELP IMAGE ATTACHED!!

a) Write a polynomial expression for the area of the shaded portion of the figure b) The area of the shaded portion is indicated above the figure . Find the area of the larger and smaller rectangles

A) A polynomial expression for the area of the shaded portion of the figure is ?

B) The area of the larger rectangle is ? Sq in.

C) The area of the smaller rectangle is ? Sq in.

Answer 1

A. (2x + 6)(x + 5) − 2x²

B. (2x + 6)(x + 5)

C. 2x²

Explanation:

The area of a rectangle is defined as:

length · width

B) We can use this to construct an equation that models the area of the large rectangle.

A = length · width

Area of large rect. = (2x + 6)(x + 5)

C) Applying the same concept to the small rectangle:

Area of small rect. = 2x(x) = 2x²

A) Finally, we can figure out the area of the shaded area by subtracting the area of the non-shaded small rectangle from the area of the large rectangle.

Area shaded = (Area of large rect.) − (Area of small rect.)

Area shaded = (2x + 6)(x + 5) − 2x²

Note: This problem doesn't specify that the answer to A needs to be simplified — it only specifies "polynomial expression" — so we can assume that it can be left unfactored.