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 \( = 7\) and width \(=3\). So, \(A_{dark}=7\times3 = 21\).

Step2: Calculate the area of the light rectangle

For the light rectangle, length \( = 7\) and width \(=x\). So, \(A_{light}=7\times x=7x\).

Step3: Calculate the area as a sum of two areas

The total area \(A_{total}=A_{dark}+A_{light}\). Substituting the values from Step 1 and Step 2, we get \(A_{total}=21 + 7x\).

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

The total length of the combined rectangle is \(7\) and the total width is \((3 + x)\). Using the area formula \(A=length\times width\), we have \(A_{total}=7\times(3 + x)=21+7x\).

Answer:

• The dark rectangle: \(21\)
• The light rectangle: \(7x\)
• As a sum of two areas: \(21 + 7x\)
• As a product of the length and width: \(7(3 + x)\) (or \(21+7x\))