the following figure is a rectangle made up of two smaller rectangles. (a) find the area of the following…

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:

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:

Answer

Explanation:

Step1: Find the area of light rectangle

The formula for the area of a rectangle is (A = length\times width). For the light - colored rectangle, the length is (7) and the width is (x). So, (A_{light}=7\times x = 7x).

Step2: Find the area of dark rectangle

For the dark - colored rectangle, the length is (7) and the width is (4). Using the area formula (A = length\times width), we get (A_{dark}=7\times4=28).

Step3: Find the area of the entire figure as a sum

The area of the entire figure as a sum of two areas is (A = A_{light}+A_{dark}=7x + 28).

Step4: Find the area of the entire figure as a product

The length of the entire rectangle is (7) and the width is ((x + 4)). Using the area formula (A=length\times width), we have (A=7\times(x + 4)).

Answer:

(a) Light rectangle: (7x); Dark rectangle: (28) (b) As a sum: (7x+28); As a product: (7(x + 4))