Question

real numbers
writing algebraic expressions for the area of a figure
e 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 check

Explanation:

Step1: Area of dark rectangle

The dark rectangle has length 9 and height \( x \). The formula for the area of a rectangle is \( \text{length} \times \text{height} \), so its area is \( 9 \times x = 9x \).

Step2: Area of light rectangle

The light rectangle has length 9 and height 5. Using the rectangle area formula, its area is \( 9 \times 5 = 45 \).

Step3: Sum of two areas (entire figure)

To find the area as the sum of the two smaller rectangles, we add their areas: \( 9x + 45 \).

Step4: Product of length and width (entire figure)

The entire figure is a rectangle with length 9 and height \( x + 5 \) (since the total height is the sum of \( x \) and 5). Using the area formula, the area is \( 9 \times (x + 5) \).

Answer:

(a) The dark rectangle: \( 9x \); The light rectangle: \( 45 \)
(b) As a sum of two areas: \( 9x + 45 \); As a product of the length and width: \( 9(x + 5) \)