Calculating the Surface Area of a Square Prism
To find the surface area of a square prism, we need to consider both the lateral surface area and the areas of the two square bases. Here’s how we can break it down step by step:
Step 1: Understand the dimensions
In this case, the square base has dimensions of:
- Base length (l) = 5 cm
- Base width (w) = 5 cm
- Height (h) = 10 cm
Step 2: Calculate the area of the base
The area of one square base can be calculated using the formula:
Area of base = l × w
Substituting in the values:
Area of base = 5 cm × 5 cm = 25 cm²
Step 3: Calculate the lateral surface area
The lateral surface area of a prism can be calculated with the formula:
Lateral Surface Area = Perimeter of base × Height
The perimeter (P) of the square base is:
P = 4 × side length = 4 × 5 cm = 20 cm
Using the height:
Lateral Surface Area = Perimeter × Height = 20 cm × 10 cm = 200 cm²
Step 4: Calculate total surface area
The total surface area (TSA) of the prism is the sum of the lateral surface area and the areas of both bases:
TSA = Lateral Surface Area + 2 × Area of base
TSA = 200 cm² + 2 × 25 cm²
TSA = 200 cm² + 50 cm² = 250 cm²
Conclusion
Therefore, the surface area of the square prism with a base measuring 5 cm by 5 cm and a height of 10 cm is 250 cm².