Kathy has a rectangular field that is 900 ft wide. One portion of the field is 9 x ft long. The other portion of the field is 14 y feet long.

Question

Use the distributive property to find an expression for the area of this field.

Answer 1

So at one end of the field it is 9 feet wide and 14 feet wide at the other.

So the field is divided into 2 parts.

The first is a rectangle 9 feet x 900 feet
The second is a triangle 900 feet x (14-9) feet
or 900 feet x 5 feet.

The area of the rectangular portion is 8100 square feet.
The are of the triangular portion is 1/2 * 5 * 900 square feet
= 5 * 450 = 2250 square feet

The total area is 3150 square feet

To address the distributive portion of the problem, it appears in
the area of the triangular portion of the field as:
1/2 * 900 * (14-9) = 1/2 * 900 * ( 10 + 4 - 9)
= 1/2 * 900 * 5
= 1/2 * 4500
= 2250

 So at one end of the field it is 9 feet wide and 14 feet wide at the other.

 

 So the field is divided into 2 parts.

 

  The first is a rectangle 9 feet x 900 feet

  The second is a triangle 900 feet x (14-9) feet 

                                 or 900 feet x 5 feet.

 

 The area of the rectangular portion is 8100 square feet.

 The are of the triangular portion is 1/2 * 5 * 900 square feet

                                                 = 5 * 450 = 2250 square feet

 

The total area is 3150 square feet

 

To address the distributive portion of the problem, it appears in 

the area of the triangular portion of the field as:

  1/2 * 900 * (14-9) = 1/2 * 900 * ( 10 + 4 - 9) 

                              = 1/2 * 900 * 5 

                              = 1/2 * 4500

                              = 2250