Question

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.
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?

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.
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.

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.

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.

Answer 1

Answer:

He is incorrect. The path will have an area of (4)(40) = 160 ft². The yard has an area of 600 ft². The area of the lawn will be the difference of the yard and path, so it is 440 ft².

Step-by-step explanation:

1. Original area of yard

A = lw = 40 × 15 = 600 ft²

2. Area of path

The path is a parallelogram.

A = bh = 4 × 40 =160 ft²

3. Remaining area

Remaining area = original area - area of path = 600 - 160 = 440 ft².