Surface area practice worksheet for cubes, prisms, and pyramids with labeled diagrams and dimensions.

Let's solve each of the surface area problems step by step. The image contains four different 3D shapes, and we are to find the surface area of each.

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1) Rectangular Prism (Net)

Given:
- Dimensions:
- Length = 10 in
- Width = 6 in
- Height = 4 in

This is a rectangular prism with a net shown. A rectangular prism has 6 faces: 2 of each type (top/bottom, front/back, left/right).

We calculate the area of each pair of faces:

- Top & Bottom: $ 10 \times 6 = 60 $ in² → two of them → $ 2 \times 60 = 120 $
- Front & Back: $ 10 \times 4 = 40 $ in² → two of them → $ 2 \times 40 = 80 $
- Left & Right: $ 6 \times 4 = 24 $ in² → two of them → $ 2 \times 24 = 48 $

Now add all:
$$
\text{Surface Area} = 120 + 80 + 48 = \boxed{248} \text{ in}^2
$$

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2) Another Rectangular Prism

Given:
- Dimensions:
- Length = 10 cm
- Width = 5 cm
- Height = 7 cm

Again, rectangular prism.

- Top & Bottom: $ 10 \times 5 = 50 $ cm² → $ 2 \times 50 = 100 $
- Front & Back: $ 10 \times 7 = 70 $ cm² → $ 2 \times 70 = 140 $
- Left & Right: $ 5 \times 7 = 35 $ cm² → $ 2 \times 35 = 70 $

Total:
$$
\text{Surface Area} = 100 + 140 + 70 = \boxed{310} \text{ cm}^2
$$

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3) Triangular Prism

Given:
- Triangle base: equilateral triangle with side = 10 ft
- Height of triangle: 8.7 ft
- Length (depth) of prism: 15 ft

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

#### Step 1: Area of one triangular base
$$
\text{Area} = \frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times 10 \times 8.7 = 43.5 \text{ ft}^2
$$
Two bases: $ 2 \times 43.5 = 87 $ ft²

#### Step 2: Lateral faces (rectangles)
Each rectangle has width = 10 ft (side of triangle), length = 15 ft

There are three such rectangles:
$$
3 \times (10 \times 15) = 3 \times 150 = 450 \text{ ft}^2
$$

#### Total Surface Area:
$$
87 + 450 = \boxed{537} \text{ ft}^2
$$

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4) Square Pyramid

Given:
- Base: square with side = 8 in
- Slant height = 5 in (from apex to midpoint of base edge)

A square pyramid has:
- 1 square base
- 4 triangular faces

#### Step 1: Area of base
$$
8 \times 8 = 64 \text{ in}^2
$$

#### Step 2: Area of one triangular face
Each triangle has:
- Base = 8 in
- Height = slant height = 5 in

$$
\text{Area} = \frac{1}{2} \times 8 \times 5 = 20 \text{ in}^2
$$

Four triangles: $ 4 \times 20 = 80 $ in²

#### Total Surface Area:
$$
64 + 80 = \boxed{144} \text{ in}^2
$$

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✔ Final Answers:

1) 248 in²
2) 310 cm²
3) 537 ft²
4) 144 in²

Let me know if you'd like this explained with diagrams or formulas!