Question

watch the video first!
find the total surface area of this triangular prism
in cm²
*hint: remember the triangle is always the true
base (bottom)

Explanation:

Step1: Identify the shape (triangular prism)

A triangular prism has 2 triangular bases and 3 rectangular faces.

Step2: Calculate area of triangular bases

The triangle has base \( 6 \, \text{cm} \) and height \( 4 \, \text{cm} \). Area of one triangle: \( \frac{1}{2} \times 6 \times 4 = 12 \, \text{cm}^2 \). Two triangles: \( 2 \times 12 = 24 \, \text{cm}^2 \).

Step3: Calculate area of rectangular faces

• Face 1: \( 6 \times 12 = 72 \, \text{cm}^2 \)
• Face 2: \( 5 \times 12 = 60 \, \text{cm}^2 \)
• Face 3: \( 5 \times 12 = 60 \, \text{cm}^2 \)

Sum of rectangles: \( 72 + 60 + 60 = 192 \, \text{cm}^2 \)

Step4: Total surface area

Add triangles and rectangles: \( 24 + 192 = 216 \, \text{cm}^2 \)

Answer:

\( 216 \)