Question

In the figure shown at right, the area of the large rectangle is (5x)(8x+1) and the area of the small rectangle is (4x)(2x) which of the following expression represents the area of the shaded region?

Answer 1

Given:

Area of large rectangle = (8x + 1)(5x)

Area of small rectangle = (4x)(2x)

To find area of the shaded region, subtract the area of the small rectangle from the large rectangle.

We have:

Area of large rectangle =

`\begin{gathered} (8x+1)(5x) \\ \\ =8x(5x)+1(5x) \\ \\ =40x^2+5x \end{gathered}`

Area of small rectangle =

`\begin{gathered} (4x)(2x) \\ \\ =8x^2 \end{gathered}`

Area of shaded region =

`\begin{gathered} (40x^2+5x)-(8x^2) \\ \\ 40x^2+5x-8x^2 \\ \\ \text{Combine like terms:} \\ 40x^2-8x^2+5x \\ \\ =32x^2+5x \end{gathered}`

Therefore, the area of the shaded region is = 32x² + 5x

ANSWER:

`32x^(2)+5x`