The area of the deck is 413 square feet
Start by calculating the area of the outer rectangle using:
Area = Length * Width
This gives
Area1 = (18 + 12) * (16 + 8)
Area1 = 720
Next, calculate the area of the inner rectangle using:
Area = Length * Width
This gives
Area2 = 16 * (18 + 8)
Area2 = 416
Subtract these areas
A1 = Area1 - Area2
A1 = 720 - 416
A1 = 304
Next, calculate the area of the outer semicircle using:
Area = 0.5πR²
This gives
Area1 = 0.5 * 3 * (12-1)²
Area1 = 181.5
Next, calculate the area of the inner semicircle using:
Area = 0.5πr²
This gives
Area2 = 0.5 * 3 * (7)²
Area2 = 73.5
Subtract these areas
A2 = Area1 - Area2
A2 = 181.5 - 73.5
A2 = 108
Add A1 and A2
A = 304 + 108
Evaluate the sum
A = 412
Hence, the area of the deck is 413 square feet
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