(a) find the area of the following (in square units).\nthe dark rectangle (on the top):\nthe light rectangle…

(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:

(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 is (x) and width is (6). So the area is (6x).

Step2: Calculate the area of the light rectangle

For the light rectangle, length is (5) and width is (6). Using the area formula (A = length\times width), we get (6\times5=30).

Step3: Calculate the area as a sum of two areas

The total area as a sum is the area of the dark rectangle plus the area of the light rectangle. So it is (6x + 30).

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

The total length of the combined rectangle is ((x + 5)) and the width is (6). Using the area formula (A=(x + 5)\times6=6(x + 5))

Answer:

  • The dark rectangle: (6x)
  • The light rectangle: (30)
  • As a sum of two areas: (6x+30)
  • As a product of the length and width: (6(x + 5))