Roy wants to make a path from one corner of his yard to the other as shown below. The path will be 4 feet wide. He wants to find the area of lawn that remains. A rectangle has a height of 40 feet and a base of 15 feet. A 4 feet wide path forms a parallelogram inside of the rectangle. Roy claims that the area of the lawn is 300 square feet since it covers exactly one-half of the yard. Which statement about his claim is correct?

Options

(A)He is incorrect. The path will have an area of (4)(40)=160 sq ft. The yard has an area of 600 sq ft. The area of the lawn will be the difference of the yard and path, so it is 440 sq ft.

(B)He is incorrect. The path will have an area of 1/2(4)(40)=80 sq ft. The yard has an area of 300 sq ft. The area of the lawn will be the difference of the yard and path, so it is 220 sq ft.

(C)He is incorrect. The path will have an area of (4)(40)=160 sq ft. The yard has an area of 300 sq ft. The area of the lawn will be the difference of the yard and path, so it is 140 sq ft.

(D)He is incorrect. The path will have an area of (9)(40)=360 sq ft. The yard has an area of 600 sq ft. The area of the lawn will be the difference of the yard and path, so it is 240 sq ft.

(A)He is incorrect. The path will have an area of (4)(40)=160 sq ft. The yard has an area of 600 sq ft. The area of the lawn will be the difference of the yard and path, so it is 440 sq ft.

Step-by-step explanation:

The diagram is attached below.

From the diagram,

The path of width 4 feet divides the yard into two triangles of base 11 feet and height 40 feet respectively. (See the second diagram).

Therefore:

Area of the lawn = 2(Area of One Triangle)

=2(0.5 X 11 X 40)

Therefore, Roy is Incorrect.

The correct option is A.

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