To find the total surface area of a rectangular prism, you can use the formula:
\[ \text{Surface Area} = 2lw + 2lh + 2wh \]
where:
- \( l \) = length
- \( w \) = width
- \( h \) = height
Given the dimensions of the box:
- Width (\( w \)) = 10 inches
- Length (\( l \)) = 9 inches
- Height (\( h \)) = 3 inches
Now, we can calculate each area:
-
Area of the Left Side (Width x Height): \[ = w \times h = 10 , \text{inches} \times 3 , \text{inches} = 30 , \text{square inches} \]
-
Area of the Back (Length x Height): \[ = l \times h = 9 , \text{inches} \times 3 , \text{inches} = 27 , \text{square inches} \]
-
Area of the Bottom (Length x Width): \[ = l \times w = 9 , \text{inches} \times 10 , \text{inches} = 90 , \text{square inches} \]
Now, we can find the total surface area:
-
The total surface area is calculated as: \[ \text{Total Surface Area} = 2lw + 2lh + 2wh \]
Plugging in the values: \[ = 2(9 \times 10) + 2(9 \times 3) + 2(10 \times 3) \] \[ = 2(90) + 2(27) + 2(30) \] \[ = 180 + 54 + 60 = 294 , \text{square inches} \]
So, you can fill out the answers as follows:
- Area of the Left Side = 30 square inches
- Area of the Back = 27 square inches
- Area of the Bottom = 90 square inches
- TOTAL surface area of the figure = 294 square inches