Question

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 light rectangle has length 4 and height \( x \). The formula for the area of a rectangle is \( \text{length} \times \text{height} \), so its area is \( 4 \times x = 4x \).

Step2: Area of dark rectangle

The dark rectangle has length 4 and height 9. Using the rectangle area formula, its area is \( 4 \times 9 = 36 \).

Step3: Area as sum of two areas

To find the total area as the sum of the two smaller rectangles' areas, we add the area of the light rectangle and the dark rectangle. So that's \( 4x + 36 \).

Step4: Area as product of length and width

The total length of the entire rectangle (height) is \( x + 9 \) and the width is 4. Using the rectangle area formula (length × width), the area is \( 4 \times (x + 9) = 4(x + 9) \) (which can also be expanded to \( 4x + 36 \), matching the sum method).

Answer:

(a) The light rectangle: \( 4x \) square units; The dark rectangle: \( 36 \) square units.
(b) As a sum of two areas: \( 4x + 36 \) square units; As a product of the length and width: \( 4(x + 9) \) (or \( 4x + 36 \)) square units.