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

Step2: Calculate the area of the light rectangle

For the light rectangle, length \(= 5\) and width \(= 8\). Using the area formula \(A = length\times width\), we get \(A_{light}=5\times8 = 40\).

Step3: Calculate the area as a sum of two areas

The total area \(A_{total - sum}=A_{dark}+A_{light}\). Substituting the values from Step1 and Step2, we have \(A_{total - sum}=8x + 40\).

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

The total length of the big rectangle is \((x + 5)\) and the width is \(8\). Using the area formula \(A=length\times width\), we get \(A_{total - product}=8(x + 5)\).

Answer:

• The dark rectangle: \(8x\)
• The light rectangle: \(40\)
• As a sum of two areas: \(8x+40\)
• As a product of the length and width: \(8(x + 5)\)