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: Find area of light rectangle

The light rectangle has length 8 and width 3. Area of rectangle is \( \text{length} \times \text{width} \), so \( 8 \times 3 = 24 \).

Step2: Find area of dark rectangle

The dark rectangle has length \( x \) and width 3. Area is \( 3 \times x = 3x \).

Step3: Sum of two areas (part b)

Add the areas of light and dark rectangles: \( 24 + 3x \).

Step4: Product of length and width (part b)

The entire rectangle has width 3 and length \( 8 + x \). Area is \( 3 \times (8 + x) = 24 + 3x \).

Answer:

(a) The light rectangle: \( 24 \); The dark rectangle: \( 3x \)
(b) As a sum: \( 24 + 3x \); As a product: \( 3(8 + x) \) (or \( 24 + 3x \))