The base of a prism is a square of side 10 cm . Find the T.S.A of the prism , if height is 12 cm .

Answer

To find the total surface area (T.S.A) of a square prism with a base side of 10 cm and a height of 12 cm, we can follow these steps:

### Step 1: Identify the dimensions of the prism.
- The base of the prism is a square with a side length of 10 cm.
- The height of the prism is 12 cm.

### Step 2: Calculate the area of the base.
- The area of the square base (A) can be calculated using the formula:
\[ A = \text{side} \times \text{side} = 10 \, \text{cm} \times 10 \, \text{cm} = 100 \, \text{cm}^2 \]

### Step 3: Calculate the total area of the two bases.
- Since there are two square bases, the total area of the bases is:
\[ \text{Total area of bases} = 2 \times A = 2 \times 100 \, \text{cm}^2 = 200 \, \text{cm}^2 \]

### Step 4: Calculate the area of the rectangular faces.
- The prism has 4 rectangular faces. The area of one rectangular face can be calculated using the formula:
\[ \text{Area of one rectangle} = \text{length} \times \text{height} = 10 \, \text{cm} \times 12 \, \text{cm} = 120 \, \text{cm}^2 \]
- Therefore, the total area of the 4 rectangular faces is:
\[ \text{Total area of rectangles} = 4 \times \text{Area of one rectangle} = 4 \times 120 \, \text{cm}^2 = 480 \, \text{cm}^2 \]

### Step 5: Calculate the total surface area of the prism.
- The total surface area (T.S.A) of the prism is the sum of the area of the bases and the area of the rectangular faces:
\[ \text{T.S.A} = \text{Total area of bases} + \text{Total area of rectangles} = 200 \, \text{cm}^2 + 480 \, \text{cm}^2 = 680 \, \text{cm}^2 \]

### Final Answer:
The total surface area of the prism is \( \text{T.S.A} = 680 \, \text{cm}^2 \).

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