Surface Area Worksheet 6th Grade - Free Printable

Let's solve each problem step by step to find the surface area of each triangular prism.

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🔷 Surface Area of a Triangular Prism Formula:

A triangular prism has:
- 2 triangular bases
- 3 rectangular faces

So,
> Surface Area = 2 × (Area of triangle) + (Sum of areas of 3 rectangles)

We'll use:
- Area of triangle = $ \frac{1}{2} \times \text{base} \times \text{height} $
- Area of rectangle = $ \text{length} \times \text{width} $

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## ✔ Problem 1:

Given:
- Triangle base = 3 cm
- Height of triangle = 2 cm
- Rectangles:
- Two identical rectangles with dimensions: 6 cm × 2.5 cm
- One rectangle: 6 cm × 3 cm (the base)

Wait — let's carefully analyze the diagram.

From the image:
- The triangular ends are isosceles triangles.
- Base of triangle = 3 cm
- Height of triangle = 2 cm
- The rectangles:
- Two rectangles of size 6 cm × 2.5 cm → these are the sides
- One rectangle of size 6 cm × 3 cm → this is the base

But wait — the two rectangles on the sides have width = 2.5 cm, which is the slant side of the triangle.

So:
- The three rectangular faces are:
- 2 rectangles: 6 cm × 2.5 cm (side faces)
- 1 rectangle: 6 cm × 3 cm (base face)

✔ So:
- Area of one triangle = $ \frac{1}{2} \times 3 \times 2 = 3 \, \text{cm}^2 $
- Two triangles: $ 2 \times 3 = 6 \, \text{cm}^2 $
- Rectangle 1: $ 6 \times 2.5 = 15 \, \text{cm}^2 $
- Rectangle 2: $ 6 \times 2.5 = 15 \, \text{cm}^2 $
- Rectangle 3: $ 6 \times 3 = 18 \, \text{cm}^2 $

Total surface area = $ 6 + 15 + 15 + 18 = 54 \, \text{cm}^2 $

> ✔ Answer for 1): 54 cm²

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## ✔ Problem 2:

Given:
- Triangle: base = 6 in, height = 4 in
- Rectangles:
- Two rectangles: 14 in × 5 in (side faces)
- One rectangle: 14 in × 6 in (base face)

Wait — the triangle has:
- Base = 6 in
- Height = 4 in
- The other two sides of triangle are 5 in each (given as "5 in" on the slanted edges)

So:
- Area of triangle = $ \frac{1}{2} \times 6 \times 4 = 12 \, \text{in}^2 $
- Two triangles: $ 2 \times 12 = 24 \, \text{in}^2 $
- Rectangles:
- Two rectangles: $ 14 \times 5 = 70 \, \text{in}^2 $ each → total = $ 2 \times 70 = 140 $
- One rectangle: $ 14 \times 6 = 84 \, \text{in}^2 $

Total surface area = $ 24 + 140 + 84 = 248 \, \text{in}^2 $

> ✔ Answer for 2): 248 in²

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## ✔ Problem 3:

Given:
- Triangle: base = 10 cm, height = 10 cm
- The two equal sides of triangle are 13 cm each
- The three rectangles:
- Two rectangles: 12 cm × 13 cm (side faces)
- One rectangle: 12 cm × 10 cm (base face)

Check:
- Area of triangle = $ \frac{1}{2} \times 10 \times 10 = 50 \, \text{cm}^2 $
- Two triangles: $ 2 \times 50 = 100 \, \text{cm}^2 $
- Rectangles:
- Two rectangles: $ 12 \times 13 = 156 \, \text{cm}^2 $ each → total = $ 2 \times 156 = 312 $
- One rectangle: $ 12 \times 10 = 120 \, \text{cm}^2 $

Total surface area = $ 100 + 312 + 120 = 532 \, \text{cm}^2 $

> ✔ Answer for 3): 532 cm²

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## ✔ Problem 4:

Given:
- Triangle: base = 12 cm, height = 8 cm
- The two equal sides of triangle are 10 cm each (from the diagram)
- Rectangles:
- Two rectangles: 15 cm × 10 cm (side faces)
- One rectangle: 15 cm × 12 cm (base face)

Calculate:
- Area of triangle = $ \frac{1}{2} \times 12 \times 8 = 48 \, \text{cm}^2 $
- Two triangles: $ 2 \times 48 = 96 \, \text{cm}^2 $
- Rectangles:
- Two rectangles: $ 15 \times 10 = 150 \, \text{cm}^2 $ each → $ 2 \times 150 = 300 $
- One rectangle: $ 15 \times 12 = 180 \, \text{cm}^2 $

Total surface area = $ 96 + 300 + 180 = 576 \, \text{cm}^2 $

> ✔ Answer for 4): 576 cm²

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✔ Final Answers:

| Problem | Surface Area |
|--------|--------------|
| 1) | 54 cm² |
| 2) | 248 in² |
| 3) | 532 cm² |
| 4) | 576 cm² |

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📌 Summary of Steps:

For each triangular prism:
1. Find area of one triangle: $ \frac{1}{2} \times \text{base} \times \text{height} $
2. Multiply by 2 for both bases
3. Add areas of all three rectangles (each = length × width)
4. Sum all parts

Let me know if you'd like a visual explanation or help drawing the nets!