A 20-ft by 40-ft swimming pool is surrounded a deck d feet wide What the area of deck?

To find the area of the deck, we need to find the total area of the space occupied by the deck and then subtract the area of the swimming pool.

The total area of the space occupied by the deck can be calculated as the sum of the areas of the four sides of the pool. Each side of the pool is (20 + 2d) feet long and d feet wide. So the total area of the deck is:

Area of deck = 2(20 + 2d) * d

= 40d + 4d^2

The area of the swimming pool is simply 20 * 40 = 800 square feet.

Therefore, the area of deck is:

Area of deck = 40d + 4d^2 - 800 square feet.