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

the following figure is a rectangle made up of two smaller rectangles.\n(a) find the area of the following (in square units).\nthe dark rectangle (on the top):\nthe light rectangle (on the bottom):\n(b) give the area of the entire figure (in square units) in two different ways.\nas a sum of two areas:\nas a product of the length and width:

the following figure is a rectangle made up of two smaller rectangles.\n(a) find the area of the following (in square units).\nthe dark rectangle (on the top):\nthe light rectangle (on the bottom):\n(b) give the area of the entire figure (in square units) in two different ways.\nas a sum of two areas:\nas a product of the length and width:

Answer

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 (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 length of the combined rectangle is (7), and the total width is ((3 + x)). Using the area formula (A=length\times 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: (21+7x)