Printable High School Math Tests and Worksheets - Grades 9-12 - Free Printable

To solve the problem, we need to calculate the surface area of each 3D shape shown in the image. Let's go through each shape step by step.

---

Shape 1: Rectangular Prism

#### Given:
- Length (\( l \)) = 6.5 cm
- Width (\( w \)) = 4.2 cm
- Height (\( h \)) = 3.8 cm

#### Formula for Surface Area of a Rectangular Prism:
\[
\text{Surface Area} = 2(lw + lh + wh)
\]

#### Calculation:
1. Calculate each term:
- \( lw = 6.5 \times 4.2 = 27.3 \)
- \( lh = 6.5 \times 3.8 = 24.7 \)
- \( wh = 4.2 \times 3.8 = 15.96 \)

2. Sum the products:
\[
lw + lh + wh = 27.3 + 24.7 + 15.96 = 67.96
\]

3. Multiply by 2:
\[
\text{Surface Area} = 2 \times 67.96 = 135.92 \, \text{cm}^2
\]

#### Answer:
\[
\boxed{135.92}
\]

---

Shape 2: Cube

#### Given:
- Side length (\( s \)) = 7.4 cm

#### Formula for Surface Area of a Cube:
\[
\text{Surface Area} = 6s^2
\]

#### Calculation:
1. Square the side length:
\[
s^2 = 7.4^2 = 54.76
\]

2. Multiply by 6:
\[
\text{Surface Area} = 6 \times 54.76 = 328.56 \, \text{cm}^2
\]

#### Answer:
\[
\boxed{328.56}
\]

---

Shape 3: Triangular Prism

#### Given:
- Base of triangle (\( b \)) = 8 cm
- Height of triangle (\( h_{\text{triangle}} \)) = 6 cm
- Length of prism (\( l \)) = 10 cm

#### Formula for Surface Area of a Triangular Prism:
\[
\text{Surface Area} = \text{Base Area} \times 2 + \text{Perimeter of Base} \times \text{Length}
\]

#### Step 1: Calculate the Base Area of the Triangle
\[
\text{Base Area} = \frac{1}{2} \times b \times h_{\text{triangle}} = \frac{1}{2} \times 8 \times 6 = 24 \, \text{cm}^2
\]

#### Step 2: Calculate the Perimeter of the Base Triangle
Assume the triangle is a right triangle (since no other sides are given):
- Hypotenuse (\( c \)) can be calculated using the Pythagorean theorem:
\[
c = \sqrt{b^2 + h_{\text{triangle}}^2} = \sqrt{8^2 + 6^2} = \sqrt{64 + 36} = \sqrt{100} = 10 \, \text{cm}
\]
- Perimeter of the base triangle:
\[
\text{Perimeter} = b + h_{\text{triangle}} + c = 8 + 6 + 10 = 24 \, \text{cm}
\]

#### Step 3: Calculate the Surface Area
1. Lateral Surface Area:
\[
\text{Lateral Surface Area} = \text{Perimeter of Base} \times \text{Length} = 24 \times 10 = 240 \, \text{cm}^2
\]

2. Total Surface Area:
\[
\text{Surface Area} = 2 \times \text{Base Area} + \text{Lateral Surface Area} = 2 \times 24 + 240 = 48 + 240 = 288 \, \text{cm}^2
\]

#### Answer:
\[
\boxed{288}
\]

---

Shape 4: Cylinder

#### Given:
- Radius (\( r \)) = 11 cm
- Height (\( h \)) = 15 cm

#### Formula for Surface Area of a Cylinder:
\[
\text{Surface Area} = 2\pi r(h + r)
\]

#### Calculation:
1. Calculate \( r + h \):
\[
r + h = 11 + 15 = 26
\]

2. Multiply by \( 2\pi r \):
\[
\text{Surface Area} = 2\pi \times 11 \times 26 = 572\pi \, \text{cm}^2
\]

Using \( \pi \approx 3.14 \):
\[
\text{Surface Area} \approx 572 \times 3.14 = 1796.08 \, \text{cm}^2
\]

#### Answer:
\[
\boxed{1796.08}
\]

---

Shape 5: Rectangular Prism

#### Given:
- Length (\( l \)) = 12.5 cm
- Width (\( w \)) = 8.3 cm
- Height (\( h \)) = 5.2 cm

#### Formula for Surface Area of a Rectangular Prism:
\[
\text{Surface Area} = 2(lw + lh + wh)
\]

#### Calculation:
1. Calculate each term:
- \( lw = 12.5 \times 8.3 = 103.75 \)
- \( lh = 12.5 \times 5.2 = 65 \)
- \( wh = 8.3 \times 5.2 = 43.16 \)

2. Sum the products:
\[
lw + lh + wh = 103.75 + 65 + 43.16 = 211.91
\]

3. Multiply by 2:
\[
\text{Surface Area} = 2 \times 211.91 = 423.82 \, \text{cm}^2
\]

#### Answer:
\[
\boxed{423.82}
\]

---

Shape 6: Triangular Prism

#### Given:
- Base of triangle (\( b \)) = 12 cm
- Height of triangle (\( h_{\text{triangle}} \)) = 9 cm
- Length of prism (\( l \)) = 15 cm

#### Formula for Surface Area of a Triangular Prism:
\[
\text{Surface Area} = \text{Base Area} \times 2 + \text{Perimeter of Base} \times \text{Length}
\]

#### Step 1: Calculate the Base Area of the Triangle
\[
\text{Base Area} = \frac{1}{2} \times b \times h_{\text{triangle}} = \frac{1}{2} \times 12 \times 9 = 54 \, \text{cm}^2
\]

#### Step 2: Calculate the Perimeter of the Base Triangle
Assume the triangle is a right triangle (since no other sides are given):
- Hypotenuse (\( c \)) can be calculated using the Pythagorean theorem:
\[
c = \sqrt{b^2 + h_{\text{triangle}}^2} = \sqrt{12^2 + 9^2} = \sqrt{144 + 81} = \sqrt{225} = 15 \, \text{cm}
\]
- Perimeter of the base triangle:
\[
\text{Perimeter} = b + h_{\text{triangle}} + c = 12 + 9 + 15 = 36 \, \text{cm}
\]

#### Step 3: Calculate the Surface Area
1. Lateral Surface Area:
\[
\text{Lateral Surface Area} = \text{Perimeter of Base} \times \text{Length} = 36 \times 15 = 540 \, \text{cm}^2
\]

2. Total Surface Area:
\[
\text{Surface Area} = 2 \times \text{Base Area} + \text{Lateral Surface Area} = 2 \times 54 + 540 = 108 + 540 = 648 \, \text{cm}^2
\]

#### Answer:
\[
\boxed{648}
\]

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Final Answers:

1. \( \boxed{135.92} \)
2. \( \boxed{328.56} \)
3. \( \boxed{288} \)
4. \( \boxed{1796.08} \)
5. \( \boxed{423.82} \)
6. \( \boxed{648} \)