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 rectangle area formula

The area of a rectangle is given by \( A = \text{length} \times \text{width} \). For the light rectangle, the length is 3 and the width is 4.

Step2: Calculate the area

Using the formula, \( A = 3 \times 4 = 12 \).

Dark Rectangle (Right)

Step1: Recall rectangle area formula

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

Step2: Calculate the area

Using the formula, \( A = 4 \times x = 4x \).

Part (b)

As a sum of two areas

Step1: Identify the two areas

The entire figure's area is the sum of the area of the light rectangle and the dark rectangle.

Step2: Add the two areas

From part (a), the light rectangle area is 12 and the dark is \( 4x \). So the sum is \( 12 + 4x \).

As a product of length and width

Answer:

Step1: Determine the total length and width

The total length of the entire rectangle is \( 3 + x \) (since it's made by combining the two smaller rectangles side - by - side) and the width is 4.

Step2: Calculate the area using the formula

Using the rectangle area formula \( A=\text{length}\times\text{width} \), we get \( A = 4\times(3 + x)=4(3 + x) \).

Final Answers

(a) Light rectangle: \(\boldsymbol{12}\); Dark rectangle: \(\boldsymbol{4x}\)

(b) Sum of two areas: \(\boldsymbol{12 + 4x}\); Product of length and width: \(\boldsymbol{4(3 + x)}\) (or \(12+4x\) after expanding, but factored form is also correct as a product)