Answer:
Design 1: $449.45
Design 2: $522.60
Design 3: $318.25
Design 3 as it's the cheapest
Step-by-step explanation:
Design 1
Area of a trapezoid = 1/2(a + b)h (where a and b are the bases and h is the height)
Given the slanted side = 3.5
Height = √(3.5² - 1²) = (3√5)/2
⇒ area of design 1 = 1/2(5 + 3) × (3√5)/2 = 6√5 = 13.42 m²
⇒ cost = 13.42 x 33.5 = $449.45
Design 2
Area of a triangle = 1/2 x base x height
Area of a rectangle = width x length
Area of a 6-sided regular polygon = 4 triangles + rectangle
⇒ area of design 2 = 4(1/2 × 1.4 × 2.0) + (2.5 × 4) = 15.6 m²
⇒ cost = 15.6 x 33.5 = $522.60
Design 3
Area of a trapezoid = 1/2(a + b)h (where a and b are the bases and h is the height)
⇒ area of design 3 = 1/2(3 + 2) × 2 + 1/2(3 + 1.5) × 2 = 9.5 m²
⇒ cost = 9.5 x 33.5 = $318.25
