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 \( A = \text{length} \times \text{width} \). For the light rectangle, the length is 8 and the width is 3.

Step2: Calculate the area

Using the formula, \( A = 8 \times 3 = 24 \).

Dark Rectangle (Right)

Step1: Recall area of rectangle formula

The area of a rectangle is \( A = \text{length} \times \text{width} \). For the dark rectangle, the length is 8 and the width is \( x \).

Step2: Calculate the area

Using the formula, \( A = 8\times x = 8x \).

Part (b)

As a sum of two areas

Step1: Sum the areas of the two rectangles

We found the area of the light rectangle is 24 and the dark one is \( 8x \). So the total area is the sum of these two areas.

Step2: Write the sum

Total area \( = 24 + 8x \).

As a product of length and width

Answer:

Step1: Find the total length of the big rectangle

The total length of the big rectangle is the sum of the widths of the two smaller rectangles, which is \( 3 + x \). The height (length) of the big rectangle is 8.

Step2: Calculate the area using the formula

Using the area formula for a rectangle \( A=\text{length}\times\text{width} \), we get \( A = 8\times(3 + x)=8(3 + x) \).

Final Answers

(a) Light rectangle: \(\boldsymbol{24}\); Dark rectangle: \(\boldsymbol{8x}\)
(b) Sum of two areas: \(\boldsymbol{24 + 8x}\); Product of length and width: \(\boldsymbol{8(3 + x)}\) (or expanded as \(24 + 8x\))