Detailed, hand-drawn educational diagram explaining the surface area calculation of a triangular prism in four steps, including visual representations and mathematical formulas.

Let’s carefully go through the problem step by step to find the surface area of the triangular prism.

The diagram breaks the surface area into 5 parts (but actually, a triangular prism has 5 faces: 2 triangles and 3 rectangles). The steps shown are:

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Step 1: Two triangular bases

Each triangle has:
- base = 12 cm
- height = 16 cm

Area of one triangle = ½ × base × height
= ½ × 12 × 16
= 6 × 16
= 96 cm²

Since there are two identical triangular bases:
96 × 2 = 192 cm²

✔ This matches what’s written in Step 1.

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Step 2: Bottom rectangular face

This rectangle is on the bottom of the prism. Its dimensions are:
- length = 12 cm (same as triangle base)
- width = 10 cm (depth of prism)

Area = base × height → here it’s length × depth
= 12 × 10 = 120 cm²

✔ Matches Step 2.

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Step 3: Left rectangular face (vertical side)

This rectangle connects the vertical side of the triangle (height = 16 cm) to the depth of the prism (10 cm).

So dimensions: 16 cm × 10 cm
Area = 16 × 10 = 160 cm²

✔ Matches Step 3.

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Step 4: Slanted rectangular face (hypotenuse side)

This rectangle connects the slanted side of the triangle (which we’re told is 20 cm — likely the hypotenuse) to the depth of the prism (10 cm).

Wait — hold on! In Step 4, they wrote:

> SA = bh = 10 · 20 = 200

But let’s check: if the slanted side of the triangle is 20 cm, and the depth is 10 cm, then yes — area = 20 × 10 = 200 cm²

BUT — wait a second. Let’s verify if that 20 cm is correct.

In Step 1, the triangle has legs 12 cm and 16 cm. If it’s a right triangle, then the hypotenuse should be:

√(12² + 16²) = √(144 + 256) = √400 = 20 cm

✔ So yes, the slanted side is indeed 20 cm. So Step 4 is correct: 20 × 10 = 200 cm²

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Final Step: Add all areas together

We have:

- Two triangles: 192 cm²
- Bottom rectangle: 120 cm²
- Left rectangle: 160 cm²
- Slanted rectangle: 200 cm²

Total = 192 + 120 + 160 + 200

Let’s add step by step:

192 + 120 = 312
312 + 160 = 472
472 + 200 = 672 cm²

✔ All calculations match the image.

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Final Answer:
672