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 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:

Part (a)

Light Rectangle (Left)

Step1: Recall area of rectangle formula

The area of a rectangle is given by \( \text{Area} = \text{length} \times \text{width} \). For the light rectangle, the length is \( 7 \) and the width is \( x \).

Step2: Calculate the area

Using the formula, the area is \( 7 \times x = 7x \).

Dark Rectangle (Right)

Step1: Recall area of rectangle formula

The area of a rectangle is \( \text{Area} = \text{length} \times \text{width} \). For the dark rectangle, the length is \( 7 \) and the width is \( 4 \).

Step2: Calculate the area

Using the formula, the area is \( 7 \times 4 = 28 \).

Part (b)

As a sum of two areas

Step1: Sum the areas of the two rectangles

The area of the light rectangle is \( 7x \) and the area of the dark rectangle is \( 28 \). So, the total area is the sum of these two areas.

Step2: Write the sum

The total area as a sum is \( 7x + 28 \).

As a product of length and width

Answer:

Step1: Determine the length and width of the entire figure

The entire figure is a rectangle. The total width of the entire figure is the sum of the widths of the two smaller rectangles, which is \( x + 4 \), and the length is \( 7 \).

Step2: Calculate the area using the product formula

Using the area formula for a rectangle (\( \text{Area} = \text{length} \times \text{width} \)), the area is \( 7 \times (x + 4) \).

Final Answers

(a)

• Light rectangle: \( \boldsymbol{7x} \)
• Dark rectangle: \( \boldsymbol{28} \)

(b)

• As a sum: \( \boldsymbol{7x + 28} \)
• As a product: \( \boldsymbol{7(x + 4)} \)