Question

On the coordinate plane shown, each grid unit represents 10 feet. Polygon QRST has vertices Q (10,30), R(-10, 30), S(-10, - 10), and T(10,- 10), and represents the floor plan of a room. Find the perimeter and area of the room.

Answer 1

Question:

On the coordinate plane shown, each grid unit represents 10 feet. Polygon QRST has vertices Q (10,30), R(-10, 30), S(-10, - 10), and T(10,- 10), and represents the floor plan of a room. Find the perimeter and area of the room.​

Solution:

Notice that the polygon QRST is a rectangle. The perimeter of a rectangle is the sum of the lengths of its sides. Notice that the measures that each side is:

QR = ST = 20

RS = QT = 40

then the perimeter P is:

`P\text{ = 2(20) + 2(40) = 40 + 80= 120}`

Then, we can conclude that the perimeter of the floor is :

`P\text{ = 120}`

now, the area of the rectangle is base times height, then in this case we have that the area of the given rectangle is:

`A\text{ = 20 x 40 = 800}`

Then, we can conclude that the area of the floor is :

`A\text{ = 800}`