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 top):
the dark 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 light rectangle

The formula for the area of a rectangle is \( \text{Area} = \text{length} \times \text{width} \). For the light rectangle, length is 3 and width is 4. So, \( 3 \times 4 = 12 \).

Step2: Area of dark rectangle

For the dark rectangle, length is 3 and width is \( x \). Using the area formula, \( 3 \times x = 3x \).

Step3: Area as sum of two areas

To find the total area as the sum of the two rectangles' areas, we add the area of the light rectangle and the dark rectangle. So, \( 12 + 3x \).

Step4: Area as product of length and width

The total length of the entire rectangle (height) is \( 4 + x \) and the width is 3. Using the area formula for the entire rectangle, \( 3 \times (4 + x) = 12 + 3x \) (which is the same as the sum, as expected).

Answer:

(a) The light rectangle: \( 12 \)
The dark rectangle: \( 3x \)

(b) As a sum of two areas: \( 12 + 3x \)
As a product of length and width: \( 3(4 + x) \) (or \( 12 + 3x \))