The cross section section of a uniform prism is a right-angled triangle with sides 3cm. 4cm and 5cm. If its length is 10cm. Calculate the total surface area

Analyze the question: A triangular prism has a right-angled triangle (3, 4, 5 cm) as its cross section, and its length is 10 cm. We need the total surface area.

Concept: Total surface area = 2 × (area of triangular end) + (perimeter of triangle × length)

The two triangular ends are identical. The three rectangular faces together form a rectangle whose width is the perimeter of the triangle and whose length is the prism's length.

Solution:

1. Area of one triangular end = ½ × base × height = ½ × 3 × 4 = 6 cm²
2. Area of the two ends = 2 × 6 = 12 cm²
3. Perimeter of the triangle = 3 + 4 + 5 = 12 cm
4. Area of the three rectangular faces = 12 × 10 = 120 cm²
5. Total surface area = 12 + 120 = 132 cm²

Check by faces: 3×10 = 30, 4×10 = 40, 5×10 = 50, which sum to 120. Adding the 12 from the two ends gives 132.

Tip: For any prism, use the formula: TSA = 2 × (end area) + (perimeter of end × length). Always remember to add the two end faces, as many students forget them and pick 120.