Question

(a) find the area of the following (in square units).
the dark rectangle (on the top):
the light 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: Calculate the area of the dark rectangle

The formula for the area of a rectangle is \(A = length\times width\). For the dark rectangle, length is \(x\) and width is \(6\). So the area is \(6x\).

Step2: Calculate the area of the light rectangle

For the light rectangle, length is \(5\) and width is \(6\). Using the area formula \(A = length\times width\), we get \(6\times5=30\).

Step3: Calculate the area as a sum of two areas

The total area as a sum is the area of the dark rectangle plus the area of the light rectangle. So it is \(6x + 30\).

Step4: Calculate the area as a product of length and width

The total length of the combined rectangle is \((x + 5)\) and the width is \(6\). Using the area formula \(A=(x + 5)\times6=6(x + 5)\)

Answer:

• The dark rectangle: \(6x\)
• The light rectangle: \(30\)
• As a sum of two areas: \(6x+30\)
• As a product of the length and width: \(6(x + 5)\)