Scenario: Landscaping Design - Learn to calculate areas and perimeters through garden and room design projects!
You're designing a backyard garden with multiple sections. You need to calculate the area for planting and the perimeter for fencing. The garden includes a rectangular lawn, a triangular flower bed, and a circular pond.
Design Challenge:
Calculate the total area and perimeter for a garden with:
• Rectangular lawn: 12 ft × 8 ft
• Triangular flower bed: base 6 ft, height 4 ft
• Circular pond: radius 3 ft
Composite garden design with multiple shapes
A = length × width
Example: 12 × 8 = 96 ft²
A = ½ × base × height
Example: ½ × 6 × 4 = 12 ft²
A = π × r²
Example: π × 3² ≈ 28.3 ft²
P = 2(length + width)
Example: 2(12 + 8) = 40 ft
P = side₁ + side₂ + side₃
Example: 6 + 5 + 5 = 16 ft
C = 2π × r
Example: 2π × 3 ≈ 18.8 ft
Rectangular Lawn: A = 12 × 8 = 96 ft²
Triangular Flower Bed: A = ½ × 6 × 4 = 12 ft²
Circular Pond: A = π × 3² = 9π ≈ 28.3 ft²
Total Area: 96 + 12 + 28.3 = 136.3 ft²
Rectangular Lawn: P = 2(12 + 8) = 40 ft
Triangular Flower Bed: P = 6 + 5 + 5 = 16 ft (assuming isosceles)
Circular Pond: C = 2π × 3 = 6π ≈ 18.8 ft
A room has an L-shaped layout. The main area is 10 ft × 12 ft, and there's a 4 ft × 6 ft extension. Find the total area and perimeter for flooring and baseboard installation.
Main Area: 10 × 12 = 120 ft²
Extension: 4 × 6 = 24 ft²
Total Area: 120 + 24 = 144 ft²
Perimeter: Calculate outer boundary = 2(16) + 2(12) = 56 ft
A rectangular patio is 15 ft long and 10 ft wide. Find the area and perimeter.
Your solution:
A garden has a 8m × 6m rectangular lawn with a 3m radius circular flower bed. Find the total area.
Your calculation: