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 light rectangle (on the left):
the dark rectangle (on the right):
(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 light rectangle

The light rectangle has length 7 and width \( x \). The formula for the area of a rectangle is \( \text{Area} = \text{length} \times \text{width} \). So, the area is \( 7 \times x = 7x \).

Step2: Area of dark rectangle

The dark rectangle has length 7 and width 6. Using the area formula for a rectangle, \( \text{Area} = 7 \times 6 = 42 \).

Step3: Area as sum of two areas

To find the area of the entire figure as the sum of the two smaller rectangles, we add their areas. So, it is \( 7x + 42 \).

Step4: Area as product of length and width

The entire figure is a rectangle with length \( x + 6 \) and width 7. Using the area formula, \( \text{Area} = 7 \times (x + 6) = 7(x + 6) \).

Answer:

(a) The light rectangle (on the left): \( 7x \)
The dark rectangle (on the right): \( 42 \)
(b) As a sum of two areas: \( 7x + 42 \)
As a product of the length and width: \( 7(x + 6) \)