If base of a prism is a square of side 4 cm, If the height of prism is 10 cm, the what will be total surface area of that prism?

Options

A. `192 cm^2`
B. `212 cm^2`
C. `214 cm^2`
D. None of the above

Answer

To find the total surface area of a prism with a square base, we can follow these steps:

### Step 1: Calculate the area of the base
The base of the prism is a square with a side length of 4 cm. The area \( A \) of a square is given by the formula:
\[ A = \text{side}^2 \]
Substituting the side length:
\[ A = 4^2 = 16 \, \text{cm}^2 \]

### Step 2: Calculate the lateral surface area
The lateral surface area (LSA) of a prism can be calculated using the formula:
\[ \text{LSA} = \text{perimeter of base} \times \text{height} \]
First, we need to find the perimeter of the square base:
\[ \text{Perimeter} = 4 \times \text{side} = 4 \times 4 = 16 \, \text{cm} \]
Now, using the height of the prism, which is 10 cm:
\[ \text{LSA} = 16 \, \text{cm} \times 10 \, \text{cm} = 160 \, \text{cm}^2 \]

### Step 3: Calculate the total surface area
The total surface area (TSA) of the prism is given by the formula:
\[ \text{TSA} = 2 \times \text{Area of base} + \text{LSA} \]
Substituting the values we calculated:
\[ \text{TSA} = 2 \times 16 \, \text{cm}^2 + 160 \, \text{cm}^2 = 32 \, \text{cm}^2 + 160 \, \text{cm}^2 = 192 \, \text{cm}^2 \]

### Final Answer
The total surface area of the prism is:
\[ \text{TSA} = 192 \, \text{cm}^2 \]