Question

real numbers
writing algebraic expressions for the area of a figure
the following figure is a rectangle made up of two smaller rectangles.
(a) find the area of the following (in square units).
the dark rectangle (on the top):
the light rectangle (on the bottom):
(b) give the area of the entire figure (in square units) in two different ways.
as a sum of two areas:
as a product of the length and width:

Explanation:

Step1: Area of dark rectangle

The formula for the area of a rectangle is \( A = \text{length} \times \text{width} \). For the dark rectangle, length is 7 and width is 2. So, \( A = 7 \times 2 = 14 \).

Step2: Area of light rectangle

For the light rectangle, length is 7 and width is \( x \). Using the area formula, \( A = 7 \times x = 7x \).

Step3: Sum of two areas (entire figure)

Add the area of the dark rectangle and the light rectangle: \( 14 + 7x \).

Step4: Product of length and width (entire figure)

The total height of the entire rectangle is \( 2 + x \) and the length is 7. So, \( A = 7 \times (2 + x) = 7(2 + x) \).

Answer:

(a) The dark rectangle: \( 14 \)
The light rectangle: \( 7x \)
(b) As a sum of two areas: \( 14 + 7x \)
As a product of length and width: \( 7(2 + x) \)