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?
To find the area of the deck, we need to subtract the area of the pool from the area of the deck including the pool.
First, let's calculate the area of the pool. The pool is rectangular and its dimensions are given as 20 feet in length and 10 feet in width. So, the area of the pool is:
Area of the pool = length × width
= 20 ft × 10 ft
= 200 square feet
Now, let's calculate the area of the deck including the pool. The deck goes around the pool and is 3 feet wide on all sides. This means that the length and width of the deck will be increased by 6 feet (3 feet on each side). So, the dimensions of the deck will be 26 feet in length (20 feet + 6 feet) and 16 feet in width (10 feet + 6 feet). The area of the deck including the pool is:
Area of the deck including the pool = length × width
= 26 ft × 16 ft
= 416 square feet
Now, to find the area of the deck only, we subtract the area of the pool from the area of the deck including the pool:
Area of the deck = Area of the deck including the pool - Area of the pool
= 416 square feet - 200 square feet
= 216 square feet
Therefore, the area of the deck is 216 square feet.
To calculate the amount of fence required to enclose the deck, we need to find the perimeter of the deck.
The perimeter of a rectangle can be calculated using the formula:
Perimeter = 2 × (length + width)
In this case, the length and width of the deck are 26 feet and 16 feet, respectively.
Perimeter of the deck = 2 × (26 ft + 16 ft)
= 2 × 42 ft
= 84 feet
Therefore, 84 feet of fence would be required to enclose the deck.
pool area: 20*10
total area: (20+6)(10+6)
that should help