Surface Area using Nets Worksheets - Free Printable

To solve the problem of finding the surface area of solids using nets, we need to count the number of unit squares in each net and then calculate the total surface area. Let's go through each shape step by step.

---

1) Rectangular Prism

- Net Description: The net shows a rectangular prism with dimensions that can be inferred from the grid.
- Counting Squares:
- There are 2 rectangles on the top and bottom (each is 3 units by 2 units).
- There are 4 rectangles on the sides (each is 3 units by 1 unit).
- Calculating Area:
- Top and Bottom: \(2 \times (3 \times 2) = 2 \times 6 = 12\)
- Sides: \(4 \times (3 \times 1) = 4 \times 3 = 12\)
- Total Surface Area: \(12 + 12 = 24\)

Surface Area = 24 square units

---

2) Cube

- Net Description: The net shows a cube with all faces being squares.
- Counting Squares:
- Each face is a square of side length 2 units.
- There are 6 faces in total.
- Calculating Area:
- Area of one face: \(2 \times 2 = 4\)
- Total Surface Area: \(6 \times 4 = 24\)

Surface Area = 24 square units

---

3) Rectangular Prism

- Net Description: The net shows a rectangular prism with dimensions that can be inferred from the grid.
- Counting Squares:
- There are 2 rectangles on the top and bottom (each is 4 units by 2 units).
- There are 4 rectangles on the sides (each is 4 units by 1 unit).
- Calculating Area:
- Top and Bottom: \(2 \times (4 \times 2) = 2 \times 8 = 16\)
- Sides: \(4 \times (4 \times 1) = 4 \times 4 = 16\)
- Total Surface Area: \(16 + 16 = 32\)

Surface Area = 32 square units

---

4) Rectangular Prism

- Net Description: The net shows a rectangular prism with dimensions that can be inferred from the grid.
- Counting Squares:
- There are 2 rectangles on the top and bottom (each is 3 units by 2 units).
- There are 4 rectangles on the sides (each is 3 units by 1 unit).
- Calculating Area:
- Top and Bottom: \(2 \times (3 \times 2) = 2 \times 6 = 12\)
- Sides: \(4 \times (3 \times 1) = 4 \times 3 = 12\)
- Total Surface Area: \(12 + 12 = 24\)

Surface Area = 24 square units

---

5) Cube

- Net Description: The net shows a cube with all faces being squares.
- Counting Squares:
- Each face is a square of side length 3 units.
- There are 6 faces in total.
- Calculating Area:
- Area of one face: \(3 \times 3 = 9\)
- Total Surface Area: \(6 \times 9 = 54\)

Surface Area = 54 square units

---

6) Triangular Prism

- Net Description: The net shows a triangular prism with two triangular bases and three rectangular lateral faces.
- Counting Squares:
- The triangular bases are equilateral triangles with side length 3 units.
- The lateral faces are rectangles with dimensions 3 units by 2 units.
- Calculating Area:
- Area of one triangular base: \(\frac{1}{2} \times \text{base} \times \text{height}\). Since it's an equilateral triangle, we can use the formula for the area of an equilateral triangle: \(\frac{\sqrt{3}}{4} \times \text{side}^2\).
- Side length = 3 units
- Area of one triangle: \(\frac{\sqrt{3}}{4} \times 3^2 = \frac{\sqrt{3}}{4} \times 9 = \frac{9\sqrt{3}}{4}\)
- Total area for two triangles: \(2 \times \frac{9\sqrt{3}}{4} = \frac{18\sqrt{3}}{4} = \frac{9\sqrt{3}}{2}\)
- Lateral Faces: There are 3 rectangles, each with dimensions 3 units by 2 units.
- Area of one rectangle: \(3 \times 2 = 6\)
- Total area for three rectangles: \(3 \times 6 = 18\)
- Total Surface Area: \(\frac{9\sqrt{3}}{2} + 18\)

Since the problem asks for the surface area in terms of unit squares, we approximate the area of the triangles:
- Each triangle has an area of approximately \(3.9\) square units (since \(\frac{9\sqrt{3}}{4} \approx 3.9\)).
- Total area for two triangles: \(2 \times 3.9 = 7.8\)
- Total Surface Area: \(7.8 + 18 = 25.8\)

For simplicity, if we consider only whole unit squares, the total surface area is approximately 26 square units.

Surface Area ≈ 26 square units

---

Final Answers

1. \(24\)
2. \(24\)
3. \(32\)
4. \(24\)
5. \(54\)
6. \(26\)

\[
\boxed{24, 24, 32, 24, 54, 26}
\]