To determine the total surface area of a three-dimensional shape, we first need to identify the shape and its dimensions. Since you haven't provided the specific shape or dimensions, I’ll guide you through the process using a general example of a rectangular prism, which can be adjusted depending on the actual figure you’re dealing with.
Step 1: Identify Faces
A rectangular prism has 6 faces (2 of each pair of opposite faces).
Step 2: Calculate the Areas of Each Face
The surface area \( SA \) of a rectangular prism is given by the formula:
\[ SA = 2lw + 2lh + 2wh \]
Where:
- \( l \) = length,
- \( w \) = width, and
- \( h \) = height.
To determine the areas mentioned in your question:
- Area of the Left Side: This is one of the side faces, calculated as: \[ \text{Area} = lh \]
- Area of the Back: This is the face at the back, calculated as: \[ \text{Area} = lw \]
- Area of the Bottom: This is the base, calculated as: \[ \text{Area} = lw \]
Step 3: Calculate the Total Surface Area
You would add the areas of all the faces. Assuming that the proper calculations have been made for each area depending on the dimensions (which we don't have), you can sum them up and perform the necessary calculations to find the total.
Example with Dimensions
Assuming an example where:
- Length \( l = 4 \) inches,
- Width \( w = 3 \) inches,
- Height \( h = 5 \) inches,
-
Area of the Left Side: \[ 5 \times 4 = 20 \text{ square inches} \]
-
Area of the Back: \[ 3 \times 4 = 12 \text{ square inches} \]
-
Area of the Bottom: \[ 4 \times 3 = 12 \text{ square inches} \]
-
Calculate Total Surface Area: \[ SA = 2lw + 2lh + 2wh = 2(4)(3) + 2(4)(5) + 2(3)(5) = 24 + 40 + 30 = 94 \text{ square inches} \]
Final Answer Format
If you provide the dimensions or the type of three-dimensional figure, I can help compute specific values. Based on this example:
- Total Faces: 6 faces
- Area of the Left Side: 20 square inches
- Area of the Back: 12 square inches
- Area of the Bottom: 12 square inches
- TOTAL Surface Area: 94 square inches
Please provide any missing details for more precise calculations!