Surface area | PDF - Free Printable

To solve the problem of finding the surface area of the given nets, we need to analyze each net individually and calculate the areas of all the shapes that make up the net. Let's go through each net step by step.

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Net 1: Triangular Prism

The net consists of:
- Two triangular faces.
- Three rectangular faces.

#### Step 1: Identify the dimensions
- The triangular faces have a base of 9 cm and a height of 12 cm.
- The rectangular faces have dimensions:
- One rectangle has dimensions 9 cm (base of the triangle) × 15 cm (length of the prism).
- Another rectangle has dimensions 15 cm × 15 cm.
- The third rectangle has dimensions 15 cm × 15 cm.

#### Step 2: Calculate the area of the triangular faces
The area of one triangular face is:
\[
\text{Area of one triangle} = \frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times 9 \times 12 = 54 \, \text{cm}^2
\]
Since there are two triangular faces:
\[
\text{Total area of triangles} = 2 \times 54 = 108 \, \text{cm}^2
\]

#### Step 3: Calculate the area of the rectangular faces
- First rectangle: \( 9 \times 15 = 135 \, \text{cm}^2 \)
- Second rectangle: \( 15 \times 15 = 225 \, \text{cm}^2 \)
- Third rectangle: \( 15 \times 15 = 225 \, \text{cm}^2 \)

#### Step 4: Sum the areas
\[
\text{Total surface area} = \text{Area of triangles} + \text{Area of rectangles}
\]
\[
\text{Total surface area} = 108 + 135 + 225 + 225 = 693 \, \text{cm}^2
\]

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Net 2: Triangular Prism

The net consists of:
- Two triangular faces.
- Three rectangular faces.

#### Step 1: Identify the dimensions
- The triangular faces have a base of 7 cm and a height of 8 cm.
- The rectangular faces have dimensions:
- One rectangle has dimensions 7 cm (base of the triangle) × 10 cm (length of the prism).
- Another rectangle has dimensions 10 cm × 8 cm.
- The third rectangle has dimensions 10 cm × 8 cm.

#### Step 2: Calculate the area of the triangular faces
The area of one triangular face is:
\[
\text{Area of one triangle} = \frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times 7 \times 8 = 28 \, \text{cm}^2
\]
Since there are two triangular faces:
\[
\text{Total area of triangles} = 2 \times 28 = 56 \, \text{cm}^2
\]

#### Step 3: Calculate the area of the rectangular faces
- First rectangle: \( 7 \times 10 = 70 \, \text{cm}^2 \)
- Second rectangle: \( 10 \times 8 = 80 \, \text{cm}^2 \)
- Third rectangle: \( 10 \times 8 = 80 \, \text{cm}^2 \)

#### Step 4: Sum the areas
\[
\text{Total surface area} = \text{Area of triangles} + \text{Area of rectangles}
\]
\[
\text{Total surface area} = 56 + 70 + 80 + 80 = 286 \, \text{cm}^2
\]

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Net 3: Rectangular Prism

The net consists of:
- Six rectangular faces.

#### Step 1: Identify the dimensions
- The dimensions of the rectangular prism are 12 cm, 14 cm, and 18 cm.
- The faces are:
- Two faces with dimensions 12 cm × 14 cm.
- Two faces with dimensions 14 cm × 18 cm.
- Two faces with dimensions 12 cm × 18 cm.

#### Step 2: Calculate the area of each pair of faces
- First pair: \( 12 \times 14 = 168 \, \text{cm}^2 \) (two faces)
- Second pair: \( 14 \times 18 = 252 \, \text{cm}^2 \) (two faces)
- Third pair: \( 12 \times 18 = 216 \, \text{cm}^2 \) (two faces)

#### Step 3: Sum the areas
\[
\text{Total surface area} = 2 \times (168 + 252 + 216)
\]
\[
\text{Total surface area} = 2 \times 636 = 1272 \, \text{cm}^2
\]

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Net 4: Triangular Prism

The net consists of:
- Two triangular faces.
- Three rectangular faces.

#### Step 1: Identify the dimensions
- The triangular faces have a base of 16 cm and a height of 7 cm.
- The rectangular faces have dimensions:
- One rectangle has dimensions 16 cm (base of the triangle) × 9 cm (length of the prism).
- Another rectangle has dimensions 9 cm × 7 cm.
- The third rectangle has dimensions 9 cm × 7 cm.

#### Step 2: Calculate the area of the triangular faces
The area of one triangular face is:
\[
\text{Area of one triangle} = \frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times 16 \times 7 = 56 \, \text{cm}^2
\]
Since there are two triangular faces:
\[
\text{Total area of triangles} = 2 \times 56 = 112 \, \text{cm}^2
\]

#### Step 3: Calculate the area of the rectangular faces
- First rectangle: \( 16 \times 9 = 144 \, \text{cm}^2 \)
- Second rectangle: \( 9 \times 7 = 63 \, \text{cm}^2 \)
- Third rectangle: \( 9 \times 7 = 63 \, \text{cm}^2 \)

#### Step 4: Sum the areas
\[
\text{Total surface area} = \text{Area of triangles} + \text{Area of rectangles}
\]
\[
\text{Total surface area} = 112 + 144 + 63 + 63 = 382 \, \text{cm}^2
\]

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Final Answers

1. Surface area of Net 1: \( \boxed{693} \, \text{cm}^2 \)
2. Surface area of Net 2: \( \boxed{286} \, \text{cm}^2 \)
3. Surface area of Net 3: \( \boxed{1272} \, \text{cm}^2 \)
4. Surface area of Net 4: \( \boxed{382} \, \text{cm}^2 \)