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 - colored rectangle

The formula for the area of a rectangle is \(A = length\times width\). For the light - colored rectangle, length \(l = 8\) and width \(w = 3\). So, \(A_{1}=8\times3=24\).

Step2: Calculate the area of the dark - colored rectangle

For the dark - colored rectangle, length \(l = 8\) and width \(w = x\). So, \(A_{2}=8\times x = 8x\).

Step3: Calculate the area of the entire figure as a sum of two areas

The area of the entire figure \(A=A_{1}+A_{2}\). Substitute \(A_{1}=24\) and \(A_{2}=8x\) into the formula. So, \(A = 24 + 8x\).

Step4: Calculate the area of the entire figure 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 get \(A=8\times(3 + x)=24+8x\).

Answer:

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