Answer:
Perimeter = 28·√2 + 24 feet
Explanation:
The dimensions of the initial sheet of plywood are;
The length of the sheet of plywood = 25 ft.
The width of the sheet of plywood = 14 ft.
The shape cut from each corner of the sheet of plywood = A right triangle
The leg length of each of the cut out right triangles = 7 ft.
The number of leg lengths of the right triangle cut from the length side of the initial sheet of plywood = 2
The length of the parallel sides of the remaining hexagonal piece of plywood = Initial length of the plywood - 2 × The leg length of the cut out right triangle
∴ The length of the parallel sides of the remaining hexagonal piece of plywood = 26 ft. - 2 × 7 ft. = 12 ft.
The other side length of the remaining hexagonal piece of plywood = The hypotenuse side of the cut out right triangle
The hypotenuse side of the cut out right triangle = √((7 ft.)² + (7 ft.)²) = 7·√2 ft.
∴ The other side length of the remaining hexagonal piece of plywood = 7·√2
The number of side lengths in the remaining hexagonal piece of plywood = 4
The perimeter of the remaining hexagonal piece of plywood = 2 × The length of the parallel sides + 4 × The other side lengths
∴ The perimeter of the remaining hexagonal piece of plywood = 2 × 12 ft. + 4 × 7·√2 = (28·√2 + 24) ft.
The perimeter of the remaining hexagonal piece of plywood = (28·√2 + 24) feet