You are designing a portion of your backyard for grass. You come up with the image shown. Solve using 3.14 as pi. What is the total area? Round to the nearest hundredth.
To find the total area of the irregular shape, we need to break it down into simple geometric shapes and then add them together.
1. The rectangle:
Area = length x width
Area = 6 ft x 10 ft = 60 sq ft
2. The quarter circle:
Radius = 4 ft
Area = 1/4 * π * radius^2
Area = 1/4 * 3.14 * 4 ft * 4 ft = 12.56 sq ft
3. The triangle:
Base = 6 ft
Height = 4 ft
Area = 1/2 * base * height
Area = 1/2 * 6 ft * 4 ft = 12 sq ft
Total Area = Rectangle Area + Quarter Circle Area + Triangle Area
Total Area = 60 sq ft + 12.56 sq ft + 12 sq ft
Total Area ≈ 84.56 sq ft
Therefore, the total area of the portion of the backyard designed for grass is approximately 84.56 square feet.