The surface area of the wedge is 84 ft².
Solution:
Base of the triangle = 4 ft
Height of the triangle = 3 ft
Area of the triangle = [tex]\frac{1}{2} \times \text{Base} \times \text{Height}[/tex]
[tex]=\frac{1}{2} \times {4} \times 3[/tex]
Area of the triangle = 6 ft²
Area of 2 triangles = 2 × 6 ft² = 12 ft²
Length of the top rectangle = 6 ft
Width of the top rectangle = 3 ft
Area of the rectangle = length × width
Area of the top rectangle = 6 × 3 = 18 ft²
Length of the middle rectangle = 6 ft
Width of the middle rectangle = 4 ft
Area of the middle rectangle = 6 × 4 = 24 ft²
Length of the bottom rectangle = 6 ft
Width of the bottom rectangle = 5 ft
Area of the bottom rectangle = 6 × 5 = 30 ft²
Surface area of the wedge = Area of 2 triangles + Area of the top rectangle + Area of the middle rectangle + Area of the bottom rectangle
= 12 ft² + 18 ft² + 24 ft² + 30 ft²
= 84 ft²
Hence the surface area of the wedge is 84 ft².
