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:

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 \( = 7\) and width \(=x\), so \(A_{light}=7\times x = 7x\)

Step2: Calculate the area of the dark rectangle

For the dark rectangle, length \( = 7\) and width \(=6\), so \(A_{dark}=7\times6=42\)

Step3: Calculate the area as a sum of two areas

\(A_{total}=A_{light}+A_{dark}=7x + 42\)

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

The total length of the big - rectangle is \((x + 6)\) and the width is \(7\). Using the formula \(A=length\times width\), we get \(A_{total}=7\times(x + 6)=7x+42\)

Answer:

(a) The light rectangle: \(7x\); The dark rectangle: \(42\)
(b) As a sum of two areas: \(7x + 42\); As a product of the length and width: \(7x + 42\)