Surface Area Worksheet 6th Grade - Free Printable

Let's solve each problem step by step to find the surface area of the given 3D shapes. The surface area is the total area of all the faces of a 3D shape.

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Problem 1: Net of a Rectangular Prism

We are given a net with dimensions:

- One side labeled 8 cm
- Another labeled 4 cm
- Another labeled 5 cm

This appears to be a rectangular prism (box) with dimensions:
- Length = 8 cm
- Width = 4 cm
- Height = 5 cm

A rectangular prism has 6 faces:
- Two faces of size $ 8 \times 4 $
- Two faces of size $ 8 \times 5 $
- Two faces of size $ 4 \times 5 $

Surface Area Formula:
$$
SA = 2(lw + lh + wh)
$$

Plug in values:
$$
SA = 2(8 \cdot 4 + 8 \cdot 5 + 4 \cdot 5) = 2(32 + 40 + 20) = 2(92) = 184 \text{ cm}^2
$$

✔ Answer: 184 cm²

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Problem 2: Net of a Cube

All sides are equal and labeled 11 inches.

This is a cube, so all 6 faces are squares of side 11 in.

Area of one face: $ 11 \times 11 = 121 \text{ in}^2 $

Total surface area:
$$
6 \times 121 = 726 \text{ in}^2
$$

✔ Answer: 726 in²

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Problem 3: Net of a Triangular Prism

The shape consists of:
- Two triangular bases
- Three rectangular faces

From the diagram:
- The triangle has base = 12 in, height = 8 in (from right triangle shown)
- The rectangular sides have lengths:
- One rectangle: 10 in × 12 in
- One rectangle: 10 in × 12 in? Wait — actually, let’s analyze carefully.

Wait — looking at the net:

- The two triangular ends have base = 12 in and height = 8 in.
- The three rectangles:
- One rectangle: 10 in × 12 in → this is the base of the triangle
- But wait — the other two rectangles must connect to the slanted sides.

Actually, from the net:
- The central rectangle is 10 in tall and 12 in wide → this is the side of the prism.
- But we also see two triangles on the left and right, with height 8 in and base 12 in.

But the prism has three rectangles and two triangles.

Looking closely:
- The triangular faces: base = 12 in, height = 8 in
- The rectangular faces:
- One: 10 in × 12 in → this is the bottom/base rectangle
- Two others: but we need the slant sides?

Wait — the length of the prism is 20 in (bottom rectangle is 20 in long). So the prism has length = 20 in.

So the rectangular faces are:
- Front and back: each is 10 in × 20 in? No — wait.

Let’s re-analyze:

From the net:
- There is a central rectangle of 20 in (length) × 10 in (height)
- On both sides are triangles with base 12 in and height 8 in
- But wait — the triangles are attached to the sides of the rectangle.

Wait — this looks like a triangular prism where:
- The bases are triangles with base 12 in and height 8 in
- The length (or depth) of the prism is 20 in

So:
- The two triangular bases: each has area $ \frac{1}{2} \times 12 \times 8 = 48 \text{ in}^2 $
- Total for two: $ 2 \times 48 = 96 \text{ in}^2 $

Now, the three rectangular faces:
- One rectangle: width = 12 in, length = 20 in → area = $ 12 \times 20 = 240 $
- Two other rectangles: these are the slanted sides of the triangle.

But we don’t know their widths directly.

Wait — we need the side lengths of the triangle.

The triangle has:
- Base = 12 in
- Height = 8 in

So it's an isosceles triangle, and we can compute the equal sides using Pythagoras.

Each slanted side:
$$
\text{Side} = \sqrt{(6)^2 + (8)^2} = \sqrt{36 + 64} = \sqrt{100} = 10 \text{ in}
$$

So the two equal sides are 10 in each.

Thus, the three rectangular faces:
1. Base rectangle: $ 12 \times 20 = 240 $
2. Left slanted: $ 10 \times 20 = 200 $
3. Right slanted: $ 10 \times 20 = 200 $

Total lateral area: $ 240 + 200 + 200 = 640 \text{ in}^2 $

Add triangular bases: $ 96 \text{ in}^2 $

Total surface area:
$$
640 + 96 = 736 \text{ in}^2
$$

✔ Answer: 736 in²

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Problem 4: Net of a Square Pyramid

The net shows:
- A square base of side 6 m
- Four triangular faces, each with base 6 m and height 7 m

So:
- Area of base: $ 6 \times 6 = 36 \text{ m}^2 $
- Area of one triangular face: $ \frac{1}{2} \times 6 \times 7 = 21 \text{ m}^2 $
- Four triangular faces: $ 4 \times 21 = 84 \text{ m}^2 $

Total surface area:
$$
36 + 84 = 120 \text{ m}^2
$$

✔ Answer: 120 m²

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✔ Final Answers:

| Problem | Surface Area |
|--------|--------------|
| 1) | 184 cm² |
| 2) | 726 in² |
| 3) | 736 in² |
| 4) | 120 m² |

Let me know if you'd like a visual explanation or breakdown!