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 top): the dark 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 light rectangle

The formula for the area of a rectangle is \(A = length\times width\). For the light rectangle, length \(l = 5\) and width \(w = 3\). So, \(A_{light}=3\times5\).

$$A_{light}=15$$

Step2: Calculate the area of the dark rectangle

For the dark rectangle, length \(l = x\) and width \(w = 3\). So, \(A_{dark}=3\times x\).

$$A_{dark}=3x$$

Step3: Calculate the area as a sum of two areas

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

$$A_{total}=15 + 3x$$

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

The total length of the big - rectangle is \(5 + x\) and the width is \(3\). Using the formula \(A = length\times width\), we have \(A_{total}=3\times(5 + x)\).

$$A_{total}=15+3x$$

Answer:

• The light rectangle (on the top): \(15\)
• The dark rectangle (on the bottom): \(3x\)
• As a sum of two areas: \(15 + 3x\)
• As a product of the length and width: \(15+3x\)