a rectangular swimming pool 20 feet long and 10 feet wide,is enclosed by a wooden deck that is 3 feet wide. What is the area of the deck? How much fence is required to enclose the deck?
A = (20 + 2*3)*(10 + 2*3) - 20 * 10
P = 2 * (20 + 10 + 4*3)
To find the area of the deck, we need to calculate the difference in area between the outer rectangle (including the deck) and the inner rectangle (just the pool).
First, let's find the area of the outer rectangle, including the deck:
Length = 20 feet + 2 * 3 feet (since the deck is present on both sides)
Width = 10 feet + 2 * 3 feet
Area = Length * Width
Area of the outer rectangle = (20 + 2 * 3) feet * (10 + 2 * 3) feet
Next, let's find the area of the inner rectangle, which is just the pool:
Length = 20 feet
Width = 10 feet
Area = Length * Width
Area of the inner rectangle = 20 feet * 10 feet
Finally, we subtract the area of the inner rectangle from the area of the outer rectangle to find the area of the deck:
Area of the deck = Area of the outer rectangle - Area of the inner rectangle
Now, to find the amount of fence required to enclose the deck, we need to calculate the perimeter of the outer rectangle:
Perimeter = 2 * (Length + Width)
Perimeter of the outer rectangle = 2 * (20 + 2 * 3) feet + 2 * (10 + 2 * 3) feet
Therefore, the area of the deck and the amount of fence required can be found using the above calculations.