Micah is going to paint his woodworking shop the shop is a rectangular prism the dimensions of the shop are shown in the diagram including doors what is the lateral surface area of the shop in square feet
Height =9ft base=7.9ft width=15.8ft
To calculate the lateral surface area of the shop, we need to find the area of all four sides (excluding the top and bottom faces).
The dimensions of the shop are:
Height = 9 ft
Base = 7.9 ft
Width = 15.8 ft
To find the area of each side, we need to calculate the height multiplied by the width for the front and back sides, and the base multiplied by the height for the side walls.
Front and Back sides:
Area = Height * Width = 9 ft * 15.8 ft = 142.2 ft²
Side walls:
Area = Base * Height = 7.9 ft * 9 ft = 71.1 ft² (for each side)
The total lateral surface area is the sum of all four sides:
Total Lateral Surface Area = (Area of front + Area of back) + (Area of left side + Area of right side)
Total Lateral Surface Area = (142.2 ft² + 142.2 ft²) + (71.1 ft² + 71.1 ft²)
Total Lateral Surface Area = 284.4 ft² + 142.2 ft²
Total Lateral Surface Area = 426.6 ft²
Therefore, the lateral surface area of the shop is 426.6 square feet.