To determine the total surface area of the rectangular prism described, we need to first identify the dimensions of the figure. It appears that two dimensions of the rectangle are already provided (3 inches, 9 inches, and 10 inches).
Let's assume the dimensions of the rectangular prism are:
- Length (L) = 10 inches
- Width (W) = 9 inches
- Height (H) = 3 inches
Step 1: Calculate the area of each face.
-
Area of the Left Side (Height x Depth)
- 3 inches x 9 inches = 27 square inches
-
Area of the Back (Height x Length)
- 3 inches x 10 inches = 30 square inches
-
Area of the Bottom (Length x Width)
- 10 inches x 9 inches = 90 square inches
Step 2: Calculate the surface area of all faces. The surface area of a rectangular prism can be calculated using the formula:
\[ \text{Surface Area} = 2(LW + LH + WH) \]
Where:
- L = Length
- W = Width
- H = Height
Substituting L = 10, W = 9, H = 3:
\[ \text{Surface Area} = 2(10 \cdot 9 + 10 \cdot 3 + 9 \cdot 3) \] \[ = 2(90 + 30 + 27) \] \[ = 2(147) \] \[ = 294 \text{ square inches} \]
Step 3: Determine the number of faces. A rectangular prism has 6 faces.
Final Answers:
- How many faces does this shape have? 6 faces
- Area of the Left Side = 27 square inches
- Area of the Back = 30 square inches
- Area of the Bottom = 90 square inches
- TOTAL surface area of the figure = 294 square inches