Question

the following figure is a rectangle made up of two smaller rectangles.
(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 \(A = \text{length}\times\text{width}\). For the dark rectangle, length \(l = 7\) and width \(w=3\). So, \(A_{dark}=7\times3 = 21\).

Step2: Calculate the area of the light rectangle

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

Step3: Calculate the area as a sum of two areas

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

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

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

Answer:

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