A solid is made up of two rectangular prisms how would I find the surface area of the solid? The diagram shows 3 feet on top, 6 feet on the left side, 7 feet on the bottom, 2 feet and 4 feet to the right Our teacher gave us the answer of 156 then told us to figure out how she got to that answer? Can someone show me how, or tell me how to do it? Thank you very much for any help you can give me.
To find the surface area of the solid made up of two rectangular prisms, you need to calculate the sum of the areas of all its sides.
First, let's consider the first rectangular prism. You're given the dimensions for the top, left side, bottom, and right side.
Top surface area = length × width = 3 ft × 4 ft = 12 sq ft
Left surface area = length × width = 6 ft × 7 ft = 42 sq ft
Bottom surface area = length × width = 3 ft × 4 ft = 12 sq ft
Right surface area = length × width = 6 ft × 2 ft = 12 sq ft
Now, let's consider the second rectangular prism. For this, we need to consider the dimensions of the right and left sides.
Right surface area = length × width = 7 ft × 2 ft = 14 sq ft
Left surface area = length × width = 7 ft × 4 ft = 28 sq ft
Adding up all the individual surface areas:
12 sq ft (Top) + 42 sq ft (Left) + 12 sq ft (Bottom) + 12 sq ft (Right) + 14 sq ft (Right) + 28 sq ft (Left)
= 100 sq ft + 42 sq ft + 42 sq ft + 14 sq ft + 28 sq ft
= 226 sq ft.
However, the answer you provided is 156 sq ft, which means we need to re-check our calculations.
After reviewing the given dimensions, it seems that we made a mistake while calculating the dimensions of the second rectangular prism.
Instead of:
Right surface area = length × width = 7 ft × 2 ft = 14 sq ft
Left surface area = length × width = 7 ft × 4 ft = 28 sq ft
It should be:
Right surface area = length × width = 7 ft × 4 ft = 28 sq ft
Left surface area = length × width = 7 ft × 2 ft = 14 sq ft
Now, adding up all the individual surface areas:
12 sq ft (Top) + 42 sq ft (Left) + 12 sq ft (Bottom) + 12 sq ft (Right) + 28 sq ft (Right) + 14 sq ft (Left)
= 100 sq ft + 42 sq ft + 42 sq ft + 12 sq ft + 28 sq ft + 14 sq ft
= 238 sq ft
Hence, the correct surface area of the solid is 238 square feet, not 156 square feet.