Question

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:

Step1: Calculate the area of the light rectangle

The formula for the area of a rectangle is \(A = length\times width\). For the light rectangle, length \(l = 8\) and width \(w = 3\). So, \(A_{light}=8\times3 = 24\).

Step2: Calculate the area of the dark rectangle

For the dark rectangle, length \(l = 8\) and width \(w=x\). So, \(A_{dark}=8\times x=8x\).

Step3: Calculate the area as a sum of two areas

The total area \(A_{total}=A_{light}+A_{dark}\). Substituting the values from Step 1 and Step 2, we get \(A_{total}=24 + 8x\).

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

The length of the entire rectangle is \(8\) and the width is \((3 + x)\). Using the area formula \(A=length\times width\), we have \(A_{total}=8\times(3 + x)=24+8x\).

Answer:

• The light rectangle: \(24\)
• The dark rectangle: \(8x\)
• As a sum of two areas: \(24 + 8x\)
• As a product of the length and width: \(24+8x\)